Tootfinder

On graph automorphisms related to Snort
Rylo Ashmore, Beth Ann Austin, Alfie M. Davies, Danny Dyer, William Kellough
https://arxiv.org/abs/2506.20669 https…

On graph automorphisms related to Snort
We study the outcomes of various positions of the game Snort. When played on graphs admitting an automorphism of order two that maps vertices outside of their closed neighbourhoods (called opposable graphs), the second player has a winning strategy. We give a necessary and sufficient condition for a graph to be opposable, and prove that the property of being opposable is preserved by several graph products. We show examples that a graph being second-player win does not imply that the graph is o…

In today's ISE 2025 lecture,, we will introduce SPARQL as a query language for knowledge graphs. Again, I'm trying out 'Dystopian Novels' as example knowledge graph playground. Let's see, if the students might know any of them. Wtat do you think? ;-)
#dystopia #literature

Higher-Order Graph Databases
Maciej Besta, Shriram Chandran, Jakub Cudak, Patrick Iff, Marcin Copik, Robert Gerstenberger, Tomasz Szydlo, J\"urgen M\"uller, Torsten Hoefler
https://arxiv.org/abs/2506.19661

Higher-Order Graph Databases
Recent advances in graph databases (GDBs) have been driving interest in large-scale analytics, yet current systems fail to support higher-order (HO) interactions beyond first-order (one-hop) relations, which are crucial for tasks such as subgraph counting, polyadic modeling, and HO graph learning. We address this by introducing a new class of systems, higher-order graph databases (HO-GDBs) that use lifting and lowering paradigms to seamlessly extend traditional GDBs with HO. We provide a theore…

SPARK: Graph-Based Online Semantic Integration System for Robot Task Planning
Mimo Shirasaka, Yuya Ikeda, Tatsuya Matsushima, Yutaka Matsuo, Yusuke Iwasawa
https://arxiv.org/abs/2506.20394

SPARK: Graph-Based Online Semantic Integration System for Robot Task Planning
The ability to update information acquired through various means online during task execution is crucial for a general-purpose service robot. This information includes geometric and semantic data. While SLAM handles geometric updates on 2D maps or 3D point clouds, online updates of semantic information remain unexplored. We attribute the challenge to the online scene graph representation, for its utility and scalability. Building on previous works regarding offline scene graph representations, …

Graph theory inspired anomaly detection at the LHC
Jack Y. Araz, Dimitrios Athanasakos, Mateusz Ploskon, Felix Ringer
https://arxiv.org/abs/2506.19920 http…

Graph theory inspired anomaly detection at the LHC
Designing model-independent anomaly detection algorithms for analyzing LHC data remains a central challenge in the search for new physics, due to the high dimensionality of collider events. In this work, we develop a graph autoencoder as an unsupervised, model-agnostic tool for anomaly detection, using the LHC Olympics dataset as a benchmark. By representing jet constituents as a graph, we introduce a method to systematically control the information available to the model through sparse graph c…

Vertex addition to a ball graph with application to reliability and area coverage in autonomous swarms
Calum Buchanan, Puck Rombach, James Bagrow, Hamid R. Ossareh
https://arxiv.org/abs/2506.19197

Vertex addition to a ball graph with application to reliability and area coverage in autonomous swarms
A unit ball graph consists of a set of vertices, labeled by points in Euclidean space, and edges joining all pairs of points within distance $1$. These geometric graphs are used to model a variety of spatial networks, including communication networks between agents in an autonomous swarm. In such an application, vertices and/or edges of the graph may not be perfectly reliable; an agent may experience failure or a communication link rendered inoperable. With the goal of designing robust swarm fo…

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web

The nilpotent graph of a finite0-dimensional Lie algebra
David Towers, Ismael Gutierrez, Luis Fernandez
https://arxiv.org/abs/2506.19758 https://

The nilpotent graph of a finite0-dimensional Lie algebra
Let $L$ be a finite-dimensional Lie algebra over a field $F$. In This paper we introduce the \emph{nilpotent graph} $Γ_\mathfrak{N}(L)$ as the graph whose vertices are the elements of $L \setminus \nil(L)$, where \[\nil(L) = \{x \in L \mid \langle x, y \rangle \text{ is nilpotent for all } y \in L\},\] and where two vertices $x, y$ are adjacent if the Lie subalgebra they generate is nilpotent. We give some characterizations of $\nil(L)$ and its connection with the hypercenter $Z^*(L)$, for exa…

Call Me Maybe: Enhancing JavaScript Call Graph Construction using Graph Neural Networks
Masudul Hasan Masud Bhuiyan, Gianluca De Stefano, Giancarlo Pellegrino, Cristian-Alexandru Staicu
https://arxiv.org/abs/2506.18191

Call Me Maybe: Enhancing JavaScript Call Graph Construction using Graph Neural Networks
Static analysis plays a key role in finding bugs, including security issues. A critical step in static analysis is building accurate call graphs that model function calls in a program. However, due to hard-to-analyze language features, existing call graph construction algorithms for JavaScript are neither sound nor complete. Prior work shows that even advanced solutions produce false edges and miss valid ones. In this work, we assist these tools by identifying missed call edges. Our main idea i…

On Exponential Random Graph Models with Dyadic Independence
Kayvan Sadeghi
https://arxiv.org/abs/2506.20458 https://arxiv.org/pdf/250…

On Exponential Random Graph Models with Dyadic Independence
We show that the only exponential random graph model with n nodal parameters, dyads being independent, and the natural assumption of permutation-equivariant nodal parametrization is the \b{eta} model. In addition, we show that an exponential random graph model with similar assumptions but with fewer than n block parameters is the additive stochastic block model. We also provide similar results for directed networks

Subcoloring of (Unit) Disk Graphs
Malory Marin, R\'emi Watrigant
https://arxiv.org/abs/2506.19452 https://arxiv.org/pdf/2506.1945…

Subcoloring of (Unit) Disk Graphs
A subcoloring of a graph is a partition of its vertex set into subsets (called colors), each inducing a disjoint union of cliques. It is a natural generalization of the classical proper coloring, in which each color must instead induce an independent set. Similarly to proper coloring, we define the subchromatic number of a graph as the minimum integer k such that it admits a subcoloring with k colors, and the corresponding problem k-Subcoloring which asks whether a graph has subchromatic number…

On plane cycles in geometric multipartite graphs
Marco Ricci, Jonathan Rollin, Andr\'e Schulz, Alexandra Weinberger
https://arxiv.org/abs/2506.20421 ht…

On plane cycles in geometric multipartite graphs
A geometric graph is a drawing of a graph in the plane where the vertices are drawn as points in general position and the edges as straight-line segments connecting their endpoints. It is plane if it contains no crossing edges. We study plane cycles in geometric complete multipartite graphs. We prove that if a geometric complete multipartite graph contains a plane cycle of length $t$, with $t \geq 6$, it also contains a smaller plane cycle of length at least $\lfloor t/2\rfloor + 1$. We further…

A family of graph GOSPA metrics for graphs with different sizes
Jinhao Gu, \'Angel F. Garc\'ia-Fern\'andez, Robert E. Firth, Lennart Svensson
https://arxiv.org/abs/2506.17316

A family of graph GOSPA metrics for graphs with different sizes
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also proved to satisfy the metric properties. Similarly to the graph GOSPA metric, the proposed graph GOSPA metric family also penalises the node attribute costs for assigned nodes between the two graphs, and the number of unassigned nodes. However, the proposed fam…

Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification
Georg Schindling
https://arxiv.org/abs/2506.19746 https…

Homomorphism Indistinguishability and Game Comonads for Restricted Conjunction and Requantification
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph classes, two structures agree on all homomorphism counts from the class if and only if they satisfy the same sentences in a corresponding logic. This perspective often reveals connections between the combinatorial properties of graph classes and the syntactic struc…

from my link log —
Heron: modern hardware graph reduction.
https://dl.acm.org/doi/abs/10.1145/3652561.3652564
saved 2025-05-16

WebGuard :Interpretable Malicious URL Detection via Bidirectional Fusion of HTML Subgraphs and Multi-Scale Convolutional BERT
Ye Tian, Zhang Yumin, Yifan Jia, Jianguo Sun, Yanbin Wang
https://arxiv.org/abs/2506.19356

WebGuard++:Interpretable Malicious URL Detection via Bidirectional Fusion of HTML Subgraphs and Multi-Scale Convolutional BERT
URL+HTML feature fusion shows promise for robust malicious URL detection, since attacker artifacts persist in DOM structures. However, prior work suffers from four critical shortcomings: (1) incomplete URL modeling, failing to jointly capture lexical patterns and semantic context; (2) HTML graph sparsity, where threat-indicative nodes (e.g., obfuscated scripts) are isolated amid benign content, causing signal dilution during graph aggregation; (3) unidirectional analysis, ignoring URL-HTML feat…

The optimal binding function for (cap, even hole)-free graphs
Ran Chen, Baogang Xu, Yian Xu
https://arxiv.org/abs/2506.19580 https://…

The optimal binding function for (cap, even hole)-free graphs
A {\em hole} is an induced cycle of length at least 4, an {\em even hole} is a hole of even length, and a {\em cap} is a graph obtained from a hole by adding an additional vertex which is adjacent exactly to two adjacent vertices of the hole. A graph $G$ obtained from a graph $H$ by blowing up all the vertices into cliques is said to be a clique blowup of $H$. Let $p, q$ be two positive integers with $p>2q$, let $F$ be a triangle-free graph, and let $G'$ be a clique blowup of $F$ with $ω(G')\l…

A Study of Dynamic Stock Relationship Modeling and S&P500 Price Forecasting Based on Differential Graph Transformer
Linyue Hu, Qi Wang
https://arxiv.org/abs/2506.18717

A Study of Dynamic Stock Relationship Modeling and S&P500 Price Forecasting Based on Differential Graph Transformer
Stock price prediction is vital for investment decisions and risk management, yet remains challenging due to markets' nonlinear dynamics and time-varying inter-stock correlations. Traditional static-correlation models fail to capture evolving stock relationships. To address this, we propose a Differential Graph Transformer (DGT) framework for dynamic relationship modeling and price prediction. Our DGT integrates sequential graph structure changes into multi-head self-attention via a differentia…

AutoGraph: A Knowledge-Graph Framework for Modeling Interface Interaction and Automating Procedure Execution in Digital Nuclear Control Rooms
Xingyu Xiao, Jiejuan Tong, Jun Sun, Zhe Sui, Jingang Liang, Hongru Zhao, Jun Zhao, Haitao Wang
https://arxiv.org/abs/2506.18727

AutoGraph: A Knowledge-Graph Framework for Modeling Interface Interaction and Automating Procedure Execution in Digital Nuclear Control Rooms
Digitalization in nuclear power plant (NPP) control rooms is reshaping how operators interact with procedures and interface elements. However, existing computer-based procedures (CBPs) often lack semantic integration with human-system interfaces (HSIs), limiting their capacity to support intelligent automation and increasing the risk of human error, particularly under dynamic or complex operating conditions. In this study, we present AutoGraph, a knowledge-graph-based framework designed to form…

Local Search Improvements for Soft Happy Colouring
Mohammad Hadi Shekarriz, Dhananjay Thiruvady, Asef Nazari, Wilfried Imrich
https://arxiv.org/abs/2506.19284

Local Search Improvements for Soft Happy Colouring
For $0\leq ρ\leq 1$ and a coloured graph $G$, a vertex $v$ is $ρ$-happy if at least $ρ°(v)$ of its neighbours have the same colour as $v$. Soft happy colouring of a partially coloured graph $G$ is the problem of finding a vertex colouring $σ$ that preserves the precolouring and has the maximum number of $ρ$-happy vertices. It is already known that this problem is NP-hard and directly relates to the community structure of the graphs; under a certain condition on the proportion of happiness…

A clusterability test for directed graphs
Mario R. Guarracino, Pierre Miasnikof, Alexander Y. Shestopaloff, Houyem Demni, Cristi\'an Bravo, Yuri Lawryshyn
https://arxiv.org/abs/2506.20111

A clusterability test for directed graphs
In this article, we extend a statistical test of graph clusterability, the $δ$ test, to directed graphs with no self loops. The $δ$ test, originally designed for undirected graphs, is based on the premise that graphs with a clustered structure display a mean local density that is statistically higher than the graph's global density. We posit that graphs that do not meet this necessary (but not sufficient) condition for clusterability can be considered unsuited to clustering. In such cases, ve…

I just released nugraph, a #dotnet tool for creating visual dependency graph of NuGet packages.
Installation:
dotnet tool install --global nugraph
Usage for a NuGet package:
nugraph Azure.Core
or for a .NET project:
nugraph ~/Projects/Kerberos.NET/Bruce/Bruce.csproj
Many options are available, everything is documented on https://github.com/0xced/nugraph
Enjoy!
Here's the kind of graph it generates (Azure.Core example).

https://mermaid.live/view#pako:eNqcVU2P2jAQ_StWViu1EjgBVqjNjS6raqXl0t6qXIwzSVwSO3UmAor4780HKF4wWdJcYux5z2_ezISDw1UIju-Mx-NAosAUfLKEHGQIku9JrFmeEBWRxd9SA31WGsiEPs3plHySgF-o9zmQDTaQj4_kO0jQDCEk6z1JEPPCd91YYFKuKVeZ6-04hK4sG9oa0_K__ajXPGVFsYSIaKWQFKjVBsZbEWLiP-U74zyEiJUpkkikqc_-lCxjWkgYtRD_wfO-evPJiKtUaf9h1jz1BV0Oh0O3Ph5Jpb_0vNkLWQmuVaEipN94ShfFXvJXiaAjxqEwCTrIz32BkNHnVIDEVWVm2hu3gkzpPV0yZIHsrnvZIchCKFnQNxXHQsZ0sa7yYRzrTZtCA9IV7FX-hgbyDh7Ia5UfUNpU9NPYEjwVzeyeuriW7VNN6xPBN-ZJTT-dnptpu93Sqn8AqdKxmzO-YTEUbhfvtu3Zok7gq-Ztt88yeqt-qaw_-C6xvRRuNVPUeye__0oj_jqhAU1yO9EhJAMNGEDdGDO9YcwQiQZPr2HWQbzHJCvw_42x0TVmzD42wyrFwJ4NsAz2RaaWiLtSusbVE3pRSAu5EXQh0vjC3BBpRgwRaeDceWXSxCbSJDeCAumMnAx0xkRY_Z8e2l1MIIN26bevs-Lmx7HC5Ez-UipzfNQlHP8BAAD__wMAEYyvHw

lastfm_aminer: Last.fm social graph
This network contains the social graph of last.fm, a site that provides a streaming radio service, where users can search music and get personalized recommendation. A directed edge (i,j) means that user i follows user j.
This network has 136409 nodes and 1685524 edges.
Tags: Social, Online, Unweighted

CORONA: A Coarse-to-Fine Framework for Graph-based Recommendation with Large Language Models
Junze Chen, Xinjie Yang, Cheng Yang, Junfei Bao, Zeyuan Guo, Yawen Li, Chuan Shi
https://arxiv.org/abs/2506.17281

CORONA: A Coarse-to-Fine Framework for Graph-based Recommendation with Large Language Models
Recommender systems (RSs) are designed to retrieve candidate items a user might be interested in from a large pool. A common approach is using graph neural networks (GNNs) to capture high-order interaction relationships. As large language models (LLMs) have shown strong capabilities across domains, researchers are exploring their use to enhance recommendation. However, prior work limits LLMs to re-ranking results or dataset augmentation, failing to utilize their power during candidate filtering…

RAAGedy right-angled Coxeter groups
Christopher H. Cashen, Pallavi Dani, Alexandra Edletzberger, Annette Karrer
https://arxiv.org/abs/2506.16789 https://…

RAAGedy right-angled Coxeter groups
We give criteria for deciding whether or not a triangle-free simple graph is the presentation graph of a right-angled Coxeter group that is quasiisometric to some right-angled Artin group, and, if so, producing a presentation graph for such a right-angled Artin group. We introduce two new graph modification operations, cloning and unfolding, to go along with an existing operation called link doubling. These operations change the presentation graph but not the quasiisometry type of the resulti…

medicX-KG: A Knowledge Graph for Pharmacists' Drug Information Needs
Lizzy Farrugia, Lilian M. Azzopardi, Jeremy Debattista, Charlie Abela
https://arxiv.org/abs/2506.17959

medicX-KG: A Knowledge Graph for Pharmacists' Drug Information Needs
The role of pharmacists is evolving from medicine dispensing to delivering comprehensive pharmaceutical services within multidisciplinary healthcare teams. Central to this shift is access to accurate, up-to-date medicinal product information supported by robust data integration. Leveraging artificial intelligence and semantic technologies, Knowledge Graphs (KGs) uncover hidden relationships and enable data-driven decision-making. This paper presents medicX-KG, a pharmacist-oriented knowledge gr…

On the Parameterized Complexity of Semitotal Domination on Graph Classes
Lukas Retschmeier
https://arxiv.org/abs/2506.17485 https://a…

On the Parameterized Complexity of Semitotal Domination on Graph Classes
For a given graph $G = (V, E)$, a subset of the vertices $D\subseteq V$ is called a semitotal dominating set, if $D$ is a dominating set and every vertex $v \in D$ is within distance two to another witness $v' \in D$. We want to find a semitotal dominating set of minimum cardinality. We show that the problem is $\mathrm{W}[2]$-hard on bipartite and split graphs when parameterized by the solution size $k$. On the positive side, we extend the kernelization technique of Alber, Fellows, and Niederm…

DiscoSG: Towards Discourse-Level Text Scene Graph Parsing through Iterative Graph Refinement
Shaoqing Lin, Chong Teng, Fei Li, Donghong Ji, Lizhen Qu, Zhuang Li
https://arxiv.org/abs/2506.15583

DiscoSG: Towards Discourse-Level Text Scene Graph Parsing through Iterative Graph Refinement
Vision-Language Models (VLMs) now generate discourse-level, multi-sentence visual descriptions, challenging text scene graph parsers originally designed for single-sentence caption-to-graph mapping. Current approaches typically merge sentence-level parsing outputs for discourse input, often missing phenomena like cross-sentence coreference, resulting in fragmented graphs and degraded downstream VLM task performance. To address this, we introduce a new task, Discourse-level text Scene Graph pars…

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
Sebastian Angermund
https://arxiv.org/abs/2506.19115 https://

A Two-Operator Calculus for Arithmetic-Progression Paths in the Collatz Graph
A recast of the standard residue-class analysis of the 3x+1 (Collatz) map in terms of two elementary operators on arithmetic progressions. The resulting calculus (i) splits any progression into its even and odd subsequences in a single step, (ii) gives a closed formula for every set of seeds that realises a prescribed parity word, (iii) yields a one line affine invariant that forbids trajectories consisting of infinitely many odd moves, and (iv) reduces the non-trivial-cycle problem to a pair o…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[11/11]:
- Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings
Aditya Sengar, Ali Hariri, Daniel Probst, Patrick Barth, Pierre Vandergheynst

The Origami flip graph of the $2\times n$ Miura-ori
Lumi Christensen, Thomas C. Hull, Emma O'Neil, Valentina Pappano, Natalya Ter-Saakov, Kacey Yang
https://arxiv.org/abs/2506.19700

The Origami flip graph of the $2\times n$ Miura-ori
Given an origami crease pattern $C=(V,E)$, a straight-line planar graph embedded in a region of $\mathbb{R}^2$, we assign each crease to be either a mountain crease (which bends convexly) or a valley crease (which bends concavely), creating a mountain-valley (MV) assignment $μ:E\to\{-1,1\}$. An MV assignment $μ$ is locally valid if the faces around each vertex in $C$ can be folded flat under $μ$. In this paper, we investigate locally valid MV assignments of the Miura-ori, $M_{m,n}$, an $m\ti…

Likelihood Ratio test for Poisson graph
Chen Shuyan, Liu Xin, Wang Shaoli
https://arxiv.org/abs/2506.18778 https://arxiv.org/pdf/2506…

Likelihood Ratio test for Poisson graph
Directed acyclic graphs are widely used to describe the causal effects among random variables, and the inference of those causal effects has become an popular topic in statistics and machine learning, and has wide applications in neuroinformatics, bioinformatics and so on. However, most studies focus on the estimation or inference of the directional relations among continuous random variables, those among discrete random variables have not gained much attentions. In this article we focus on the…

Multimodal Visual Image Based User Association and Beamforming Using Graph Neural Networks
Yinghan Li, Yiming Liu, Wei Yu
https://arxiv.org/abs/2506.18218 …

Multimodal Visual Image Based User Association and Beamforming Using Graph Neural Networks
This paper proposes an approach that leverages multimodal data by integrating visual images with radio frequency (RF) pilots to optimize user association and beamforming in a downlink wireless cellular network under a max-min fairness criterion. Traditional methods typically optimize wireless system parameters based on channel state information (CSI). However, obtaining accurate CSI requires extensive pilot transmissions, which lead to increased overhead and latency. Moreover, the optimization …

@… in your #clojure `ubergraph` library, there appear (unless I'm stupid) to be no functions for navigating 'down' a directed graph -- there's `(predecessors g n)` but no corresponding `(children g n)`.
Is this intentional, and is the…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Representation Stability for Marked Graph Complexes
Enoch Fedah, Benjamin C. Ward

Subgraph Entropy
Tawfiq Ahmed, Tarik Aougab, Matt Clay
https://arxiv.org/abs/2506.18838 https://arxiv.org/pdf/2506.18838

Subgraph Entropy
Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space.

Looking for Signs: Reasoning About FOBNNs Using SAT
Hans-J\"org Schurr, Ath\'ena\"is Vaginay
https://arxiv.org/abs/2506.19156 https://…

Looking for Signs: Reasoning About FOBNNs Using SAT
First-Order Boolean Networks with Non-deterministic updates (FOBNN) compute a boolean transition graph representing the absence and presence of species over time. The utility of FOBNNs has been justified by their theoretical soundness with respect to the Euler simulation of the differential equations. However, we lack practical means to work with FOBNNs and an empirical evaluation of their properties. We present a sound and efficient reduction of the first-order FOBNN transition relation to a p…

EHCube4P: Learning Epistatic Patterns Through Hypercube Graph Convolution Neural Network for Protein Fitness Function Estimation
Muhammad Daud, Philippe Charton, Cedric Damour, Jingbo Wang, Frederic Cadet
https://arxiv.org/abs/2506.16921

EHCube4P: Learning Epistatic Patterns Through Hypercube Graph Convolution Neural Network for Protein Fitness Function Estimation
Understanding the relationship between protein sequences and their functions is fundamental to protein engineering, but this task is hindered by the combinatorially vast sequence space and the experimental noise inherent in fitness measurements. In this study, we present a novel framework that models the sequence landscape as a hypercube $H(k,2)$ and integrates wavelet-based signal denoising with a graph convolutional neural network (GCN) to predict protein fitness across rugged fitness landsca…

Resonances of recurrence time of monitored quantum walks
Ruoyu Yin, Qingyuan Wang, Sabine Tornow, Eli Barkai
https://arxiv.org/abs/2506.19832 https://

Resonances of recurrence time of monitored quantum walks
The recurrence time is the time a process first returns to its initial state. Using quantum walks on a graph, the recurrence time is defined through stroboscopic monitoring of the arrival of the particle to a node of the system. When the time interval between repeated measurements is tuned in such a way that eigenvalues of the unitary become degenerate, the mean recurrence time exhibits resonances. These resonances imply faster mean recurrence times, which were recorded on quantum computers. Th…

Exact and approximate maximin share allocations in multi-graphs
George Christodoulou, Symeon Mastrakoulis
https://arxiv.org/abs/2506.20317 https://

Exact and approximate maximin share allocations in multi-graphs
We study the problem of (approximate) maximin share (MMS) allocation of indivisible items among a set of agents. We focus on the graphical valuation model, previously studied by Christodolou, Fiat, Koutsoupias, and Sgouritsa ("Fair allocation in graphs", EC 2023), where the input is given by a graph where edges correspond to items, and vertices correspond to agents. An edge may have non-zero marginal value only for its incident vertices. We study additive, XOS and subadditive valuations and we …

MM-AttacKG: A Multimodal Approach to Attack Graph Construction with Large Language Models
Yongheng Zhang, Xinyun Zhao, Yunshan Ma, Haokai Ma, Yingxiao Guan, Guozheng Yang, Yuliang Lu, Xiang Wang
https://arxiv.org/abs/2506.16968

MM-AttacKG: A Multimodal Approach to Attack Graph Construction with Large Language Models
Cyber Threat Intelligence (CTI) parsing aims to extract key threat information from massive data, transform it into actionable intelligence, enhance threat detection and defense efficiency, including attack graph construction, intelligence fusion and indicator extraction. Among these research topics, Attack Graph Construction (AGC) is essential for visualizing and understanding the potential attack paths of threat events from CTI reports. Existing approaches primarily construct the attack graph…

On Gy\'arf\'as' Path-Colour Problem
Ben Cameron, Alexander Clow
https://arxiv.org/abs/2506.19100 https://arxiv.org/pdf/25…

On Gyárfás' Path-Colour Problem
In their 1997 paper titled ``Fruit Salad", Gyárfás posed the following conjecture: there exists a constant $k$ such that if each path of a graph spans a $3$-colourable subgraph, then the graph is $k$-colourable. It is noted that $k=4$ might suffice. Let $r(G)$ be the maximum chromatic number of any subgraph $H$ of $G$ where $H$ is spanned by a path. The only progress on this conjecture comes from Randerath and Schiermeyer in 2002, who proved that if $G$ is an $n$ vertex graph, then $χ(G) \le…

Paired Disjunctive Domination Number of Middle Graphs
Hande Tuncel Golpek, Zeliha Kartal Yildiz, Aysun Aytac
https://arxiv.org/abs/2506.19529 https://

Paired Disjunctive Domination Number of Middle Graphs
The concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a transformation that captures both adjacency and incidence relations of the original graph. We begin by investigating this parameter for middle graphs of several special graph classes, including path graphs, cycle graphs, wheel graphs, complete graphs, complete bip…

DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules
Junjie Xu, Jiahao Zhang, Mangal Prakash, Xiang Zhang, Suhang Wang
https://arxiv.org/abs/2506.19862

DualEquiNet: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules
Geometric graph neural networks (GNNs) that respect E(3) symmetries have achieved strong performance on small molecule modeling, but they face scalability and expressiveness challenges when applied to large biomolecules such as RNA and proteins. These systems require models that can simultaneously capture fine-grained atomic interactions, long-range dependencies across spatially distant components, and biologically relevant hierarchical structure, such as atoms forming residues, which in turn f…

Bayesian Social Deduction with Graph-Informed Language Models
Shahab Rahimirad, Guven Gergerli, Lucia Romero, Angela Qian, Matthew Lyle Olson, Simon Stepputtis, Joseph Campbell
https://arxiv.org/abs/2506.17788

Bayesian Social Deduction with Graph-Informed Language Models
Social reasoning - inferring unobservable beliefs and intentions from partial observations of other agents - remains a challenging task for large language models (LLMs). We evaluate the limits of current reasoning language models in the social deduction game Avalon and find that while the largest models demonstrate strong performance, they require extensive test-time inference and degrade sharply when distilled to smaller, real-time-capable variants. To address this, we introduce a hybrid reaso…

Detection and Reconstruction of a Random Hypergraph from Noisy Graph Projection
Shuyang Gong, Zhangsong Li, Qiheng Xu
https://arxiv.org/abs/2506.17527 http…

Detection and Reconstruction of a Random Hypergraph from Noisy Graph Projection
For a $d$-uniform random hypergraph on $n$ vertices in which hyperedges are included i.i.d.\ so that the average degree in the hypergraph is $n^{δ+o(1)}$, the projection of such a hypergraph is a graph on the same $n$ vertices where an edge connects two vertices if and only if they belong to a same hyperedge. In this work, we study the inference problem where the observation is a \emph{noisy} version of the graph projection where each edge in the projection is kept with probability $p=n^{-1+α…

Sometimes you look at a graph and think that a particular value seems a bit odd. Then you look at the other numbers and they seem off, too. At that point, you realise that the graph is not intended to clarify, but to obscure. On German #EV charging prices, Quartets and diesel.

Sometimes you look at a graph and think that a particular value seems a… | Jaap Burger
Sometimes you look at a graph and think that a particular value seems a bit odd. Then you look at the other numbers and they seem off, too. At that point, you realise that the graph is not intended to clarify, but to obscure. Thank you, Felix Hamer, for drawing attention to this recent slide from BDEW Bundesverband der Energie- und Wasserwirtschaft e.V. The title suggests that EV charging would only cost the same as filling up a diesel or petrol car for the same distance in an 'Extremszenario…

A biophysical approach to the design of networks of communication systems
Rodrigo Almeida, Ana Filipa Valente, Rui Dil\~ao
https://arxiv.org/abs/2506.20572

A biophysical approach to the design of networks of communication systems
Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we use a formalism that describes adaptive incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within Euclidean space. These graphs are either suboptimal or optimal in terms of their length. Occasionally, we obtain graph tree configurations that are topologically equivalent to Steiner trees. This approach is employed to design communication systems, such as railway …

Empowering Iterative Graph Alignment Using Heat Diffusion
Boyan Wang, Weijie Feng, Jinyang Huang, Dan Guo, Zhi Liu
https://arxiv.org/abs/2506.17640 https:/…

Empowering Iterative Graph Alignment Using Heat Diffusion
Unsupervised plain graph alignment (UPGA) aims to align corresponding nodes across two graphs without any auxiliary information. Existing UPGA methods rely on structural consistency while neglecting the inherent structural differences in real-world graphs, leading to biased node representations. Moreover, their one-shot alignment strategies lack mechanisms to correct erroneous matches arising from inaccurate anchor seeds. To address these issues, this paper proposes IterAlign, a novel parameter…

Further detail about what's been happening expanding on my thread about context: #USpol

stanford_web: Webgraph (Stanford)
The web graph of Stanford University (stanford.edu), as collected in 2002. Nodes represent pages and directed edges represent hyperlinks between them.
This network has 281904 nodes and 2312497 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/s…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[2/3]:
- Rewarding Graph Reasoning Process makes LLMs more Generalized Reasoners
Miao Peng, Nuo Chen, Zongrui Suo, Jia Li

Climate stripes for the Netherlands. It's already almost 2°C warmer than in 1980 here, on average.
#ShowYourStripesDay

Counting edges of different types in a local graph of a Grassmann graph
Ian Seong
https://arxiv.org/abs/2506.18700 https://arxiv.org/…

Counting edges of different types in a local graph of a Grassmann graph
Let $\mathbb{F}_q$ denote a finite field with $q$ elements. Let $n,k$ denote integers with $n>2k\geq 6$. Let $V$ denote a vector space over $\mathbb{F}_{q}$ that has dimension $n$. The vertex set of the Grassmann graph $J_q(n,k)$ consists of the $k$-dimensional subspaces of $V$. Two vertices of $J_q(n,k)$ are adjacent whenever their intersection has dimension $k-1$. Let $\partial$ denote the path-length distance function of $J_q(n,k)$. Pick vertices $x,y$ of $J_q(n,k)$ such that $1<\partial(x,y…

Local Routing on Ordered $\Theta$-graphs
Andr\'e van Renssen, Shuei Sakaguchi
https://arxiv.org/abs/2506.16021 https://arxiv.org/…

Local Routing on Ordered $Θ$-graphs
The problem of locally routing on geometric networks using limited memory is extensively studied in computational geometry. We consider one particular graph, the ordered $Θ$-graph, which is significantly harder to route on than the $Θ$-graph, for which a number of routing algorithms are known. Currently, no local routing algorithm is known for the ordered $Θ$-graph. We prove that, unfortunately, there does not exist a deterministic memoryless local routing algorithm that works on the order…

Empowering Graph-based Approximate Nearest Neighbor Search with Adaptive Awareness Capabilities
Jiancheng Ruan, Tingyang Chen, Renchi Yang, Xiangyu Ke, Yunjun Gao
https://arxiv.org/abs/2506.15986

Empowering Graph-based Approximate Nearest Neighbor Search with Adaptive Awareness Capabilities
Approximate Nearest Neighbor Search (ANNS) in high-dimensional spaces finds extensive applications in databases, information retrieval, recommender systems, etc. While graph-based methods have emerged as the leading solution for ANNS due to their superior query performance, they still face several challenges, such as struggling with local optima and redundant computations. These issues arise because existing methods (i) fail to fully exploit the topological information underlying the proximity …

Towards Real-time Structural Dynamics Simulation with Graph-based Digital Twin Modelling
Jun Zhang, Tong Zhang, Ying Wang
https://arxiv.org/abs/2506.18724 …

Towards Real-time Structural Dynamics Simulation with Graph-based Digital Twin Modelling
Precise and timely simulation of a structure's dynamic behavior is crucial for evaluating its performance and assessing its health status. Traditional numerical methods are often limited by high computational costs and low efficiency, while deep learning approaches offer a promising alternative. However, these data-driven methods still face challenges, such as limited physical interpretability and difficulty in adapting to diverse structural configurations. To address these issues, this study p…

Computing Tree Structures in Anonymous Graphs via Mobile Agents
Prabhat Kumar Chand, Manish Kumar, Anisur Rahaman Molla
https://arxiv.org/abs/2506.19365 ht…

Computing Tree Structures in Anonymous Graphs via Mobile Agents
Minimum Spanning Tree (MST) and Breadth-First Search (BFS) tree constructions are classical problems in distributed computing, traditionally studied in the message-passing model, where static nodes communicate via messages. This paper investigates MST and BFS tree construction in an agent-based network, where mobile agents explore a graph and compute. Each node hosts one agent, and communication occurs when agents meet at a node. We consider $n$ agents initially dispersed (one per node) in an a…

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Nero Ziyu Li, Frank Xin Hu, Thomas Britz
https://arxiv.org/abs/2506.18073 https://

Reducible Iterated Graph Systems: multiscale-freeness and multifractals
Iterated Graph Systems (IGS) aims to transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for graph fractals, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite …

Structural Optimal Jacobian Accumulation and Minimum Edge Count are NP-Complete Under Vertex Elimination
Matthias Bentert, Alex Crane, P{\aa}l Gr{\o}n{\aa}s Drange, Yosuke Mizutani, Blair D. Sullivan
https://arxiv.org/abs/2506.17521

Structural Optimal Jacobian Accumulation and Minimum Edge Count are NP-Complete Under Vertex Elimination
We study graph-theoretic formulations of two fundamental problems in algorithmic differentiation. The first (Structural Optimal Jacobian Accumulation) is that of computing a Jacobian while minimizing multiplications. The second (Minimum Edge Count) is to find a minimum-size computational graph. For both problems, we consider the vertex elimination operation. Our main contribution is to show that both problems are NP-complete, thus resolving longstanding open questions. In contrast to prior work…

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Relative train tracks and generalized endperiodic graph maps
Yan Mary He, Chenxi Wu

Unimodular random graphs with Property (T) have cost one
{\L}ukasz Grabowski, H\'ector Jard\'on-S\'anchez, Sam Mellick
https://arxiv.org/abs/2506.19454

Unimodular random graphs with Property (T) have cost one
Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem, and extend it both to locally compact second countable groups and unimodular random graphs. We prove unimodular random graph analogues of the Connes--Weiss and Glasner--Weiss theorem characterising Property (T).

A Multi-Modal Spatial Risk Framework for EV Charging Infrastructure Using Remote Sensing
Oktay Karaku\c{s}, Padraig Corcoran
https://arxiv.org/abs/2506.19860

A Multi-Modal Spatial Risk Framework for EV Charging Infrastructure Using Remote Sensing
Electric vehicle (EV) charging infrastructure is increasingly critical to sustainable transport systems, yet its resilience under environmental and infrastructural stress remains underexplored. In this paper, we introduce RSERI-EV, a spatially explicit and multi-modal risk assessment framework that combines remote sensing data, open infrastructure datasets, and spatial graph analytics to evaluate the vulnerability of EV charging stations. RSERI-EV integrates diverse data layers, including flood…

AnyMAC: Cascading Flexible Multi-Agent Collaboration via Next-Agent Prediction
Song Wang, Zhen Tan, Zihan Chen, Shuang Zhou, Tianlong Chen, Jundong Li
https://arxiv.org/abs/2506.17784

AnyMAC: Cascading Flexible Multi-Agent Collaboration via Next-Agent Prediction
Recent progress in large language model (LLM)-based multi-agent collaboration highlights the power of structured communication in enabling collective intelligence. However, existing methods largely rely on static or graph-based inter-agent topologies, lacking the potential adaptability and flexibility in communication. In this work, we propose a new framework that rethinks multi-agent coordination through a sequential structure rather than a graph structure, offering a significantly larger topo…

Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$
Erik Panzer
https://arxiv.org/abs/2506.18788 https://arxiv.org…

Graph theoretic properties of Speyer's matroid polynomial $g_M(t)$
We prove relations between the number of $k$-connected components of a graph, Crapo's invariant $β(M)$ of a matroid, and Speyer's polynomial $g_M(t)$. These yield a simple interpretation of $g_M'(-1)$ when $M$ is graphic or cographic. Furthermore, we improve Ferroni's algorithm to compute $g_M(t)$ and provide an implementation and an extensive data set. These calculations reveal a large number of graph theoretic constraints on the second derivative $g_M''(-1)$, which we thus advertise as an in…

as_skitter: Skitter IP graph (2005)
An aggregate snapshot of the Internet Protocol (IP) graph, as measured by the traceroute tool on CAIDA's skitter infrastructure, in 2005.
This network has 1696415 nodes and 11095298 edges.
Tags: Technological, Communication, Unweighted
https://networks.skewed.de/net/as_s…

Replaced article(s) found for cs.DB. https://arxiv.org/list/cs.DB/new
[1/1]:
- Survey: Graph Databases
Miguel E. Coimbra, Lucie Svit\'akov\'a, Alexandre P. Francisco, Lu\'is Veiga

Heterogeneous Temporal Hypergraph Neural Network
Huan Liu, Pengfei Jiao, Mengzhou Gao, Chaochao Chen, Di Jin
https://arxiv.org/abs/2506.17312 https://

Heterogeneous Temporal Hypergraph Neural Network
Graph representation learning (GRL) has emerged as an effective technique for modeling graph-structured data. When modeling heterogeneity and dynamics in real-world complex networks, GRL methods designed for complex heterogeneous temporal graphs (HTGs) have been proposed and have achieved successful applications in various fields. However, most existing GRL methods mainly focus on preserving the low-order topology information while ignoring higher-order group interaction relationships, which ar…

On minors of non-hamiltonian graphs
On-Hei Solomon Lo
https://arxiv.org/abs/2506.20087 https://arxiv.org/pdf/2506.20087

On minors of non-hamiltonian graphs
A theorem of Tutte states that every 4-connected non-hamiltonian graph contains $K_{3,3}$ as a minor. We strengthen this result by proving that such a graph must contain $K_{3,4}$ as a minor, thereby confirming a special case of a conjecture posed by Chen, Yu, and Zang in a strong form. This result may be viewed as a step toward characterizing the minor-minimal 4-connected non-hamiltonian graphs. As a 3-connected analog, Ding and Marshall conjectured that every 3-connected non-hamiltonian graph…

Continuous Map Matching to Paths under Travel Time Constraints
Yannick Bosch, Sabine Storandt
https://arxiv.org/abs/2506.18354 https://

Continuous Map Matching to Paths under Travel Time Constraints
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by location in the graph, such that consecutive locations can be reached from one another along the path within the timestamp difference of the respective measurements. This problem arises in public transit data processing as well as in map matching of movement tra…

Rational Exponents for General Graphs
Sean English, Sam Spiro
https://arxiv.org/abs/2506.19061 https://arxiv.org/pdf/2506.19061

Rational Exponents for General Graphs
A rational number $r$ is a \textbf{realizable exponent} for a graph $H$ if there exists a finite family of graphs $\mathcal{F}$ such that $\mathrm{ex}(n,H,\mathcal{F})=Θ(n^r)$, where $\mathrm{ex}(n,H,\mathcal{F})$ denotes the maximum number of copies of $H$ that an $n$-vertex $\mathcal{F}$-free graph can have. Results for realizable exponents are currently known only when $H$ is either a star or a clique, with the full resolution of the $H=K_2$ case being a major breakthrough of Bukh and Conlo…

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web

Stereotype graph: A mathematical framework of category stereotypes via graph theory
Yijia Yan
https://arxiv.org/abs/2506.12533 https://

Stereotype graph: A mathematical framework of category stereotypes via graph theory
In social psychology and cognitive science, there has been much interest in studying category stereotypes. However, we still lack a consensual mathematical definition or framework, which is necessary for us to hold a deeper understanding of stereotypes in human cognition. In this paper, we use graph theory to portray category stereotypes in human cognition, based on pairs of labels having special relations. By using methods and conclusions in graph theory (including algebraic graph theory and v…

Properties and Expressivity of Linear Geometric Centralities
Paolo Boldi, Flavio Furia, Chiara Prezioso
https://arxiv.org/abs/2506.19670 https://

Properties and Expressivity of Linear Geometric Centralities
Centrality indices are used to rank the nodes of a graph by importance: this is a common need in many concrete situations (social networks, citation networks, web graphs, for instance) and it was discussed many times in sociology, psychology, mathematics and computer science, giving rise to a whole zoo of definitions of centrality. Although they differ widely in nature, many centrality measures are based on shortest-path distances: such centralities are often referred to as geometric. Geometric…

Adjacency spectral radius and H-factors in 1-binding graphs
Sizhong Zhou, Tao Zhang, Zhiren Sun
https://arxiv.org/abs/2506.20273 https://

Adjacency spectral radius and H-factors in 1-binding graphs
Let $G$ be a graph, and let $H:V(G)\longrightarrow\{\{1\},\{0,2\}\}$ be a set-valued function. Hence, $H(v)$ equals $\{1\}$ or $\{0,2\}$ for any $v\in V(G)$. We let $$ H^{-1}(1)=\{v: v\in V(G) \ \mbox{and} \ H(v)=1\}. $$ An $H$-factor of $G$ is a spanning subgraph $F$ of $G$ such that $d_F(v)\in H(v)$ for each $v\in V(G)$. Lu and Kano showed a characterization for the existence of an $H$-factor in a graph [Characterization of 1-tough graphs using factors, Discrete Math. 343 (2020) 111901]. Let …

Understanding the Effect of Knowledge Graph Extraction Error on Downstream Graph Analyses: A Case Study on Affiliation Graphs
Erica Cai, Brendan O'Connor
https://arxiv.org/abs/2506.12367

Understanding the Effect of Knowledge Graph Extraction Error on Downstream Graph Analyses: A Case Study on Affiliation Graphs
Knowledge graphs (KGs) are useful for analyzing social structures, community dynamics, institutional memberships, and other complex relationships across domains from sociology to public health. While recent advances in large language models (LLMs) have improved the scalability and accessibility of automated KG extraction from large text corpora, the impacts of extraction errors on downstream analyses are poorly understood, especially for applied scientists who depend on accurate KGs for real-wo…

Conformal Rigidity and Spectral Embeddings of Graphs
Jo\~ao Gouveia, Stefan Steinerberger, Rekha R. Thomas
https://arxiv.org/abs/2506.20541 https://…

Conformal Rigidity and Spectral Embeddings of Graphs
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular graphs are known to be conformally rigid. We establish new results using the connection between conformal rigidity and edge-isometric spectral embeddings of the graph. All $1$-walk regular graphs are conformally rigid, a consequence of a stronger property of t…

lastfm_aminer: Last.fm social graph
This network contains the social graph of last.fm, a site that provides a streaming radio service, where users can search music and get personalized recommendation. A directed edge (i,j) means that user i follows user j.
This network has 136409 nodes and 1685524 edges.
Tags: Social, Online, Unweighted

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[5/5]:
- Affordable AI Assistants with Knowledge Graph of Thoughts
Maciej Besta, et al.

google_web: Old Google web graph (2002)
A web graph representing a crawl of a portion of the general WWW, from a 2002 Google Programming contest.
This network has 916428 nodes and 5105039 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/google_web

stanford_web: Webgraph (Stanford)
The web graph of Stanford University (stanford.edu), as collected in 2002. Nodes represent pages and directed edges represent hyperlinks between them.
This network has 281904 nodes and 2312497 edges.
Tags: Informational, Web graph, Unweighted
https://networks.skewed.de/net/s…

Counter-example to Conjectures on Complemented Zero-Divisor Graphs of Semigroups
Anagha Khiste, Ganesh Tarte, Vinayak Joshi
https://arxiv.org/abs/2506.16919

Counter-example to Conjectures on Complemented Zero-Divisor Graphs of Semigroups
In this paper, we are motivated by two conjectures proposed by C. Bender et al.\ in 2024, which have remained open questions. The first conjecture states that if the complemented zero-divisor graph \( G(S) \) of a commutative semigroup \( S \) with a zero element has the clique number three or greater, then the reduced graph \( G_r(S) \) is isomorphic to the graph \( G(\mathcal{P}(n)) \). The second conjecture asserts that if \( G(S) \) is a complemented zero-divisor graph with the clique numbe…

The Hamilton cycle space of random graphs
Dan Hefetz, Michael Krivelevich
https://arxiv.org/abs/2506.19731 https://arxiv.org/pdf/2506…

The Hamilton cycle space of random graphs
The cycle space of a graph $G$, denoted $C(G)$, is a vector space over ${\mathbb F}_2$, spanned by all incidence vectors of edge-sets of cycles of $G$. If $G$ has $n$ vertices, then $C_n(G)$ denotes the subspace of $C(G)$, spanned by the incidence vectors of Hamilton cycles of $G$. A classical result in the theory of random graphs asserts that for $G \sim \mathbb{G}(n,p)$, asymptotically almost surely the necessary condition $δ(G) \geq 2$ is also sufficient to ensure Hamiltonicity. Resolving a…

The number of possibilities for random dating
Aaron Abrams, Rod Canfield, Andrew Granville
https://arxiv.org/abs/2506.20072 https://a…

The number of possibilities for random dating
Let $G$ be a regular graph and $H$ a subgraph on the same vertex set. We give surprisingly compact formulas for the number of copies of $H$ one expects to find in a random subgraph of $G$.

New upper bounds on the order of mixed cages of girth 6
Gabriela Araujo-Pardo, Lydia Mirabel Mendoza-Cadena
https://arxiv.org/abs/2506.20003 https://

New upper bounds on the order of mixed cages of girth 6
A $[z,r;g]$-mixed cage is a mixed graph of minimum order such that each vertex has $z$ in-arcs, $z$ out-arcs, $r$ edges, and it has girth $g$, and the minimum order for $[z,r;g]$-mixed graphs is denoted by $n[z,r;g]$. In this paper, we present an infinite family of mixed graphs with girth $6$, that improves, in some cases, the families that we give in G. Araujo-Pardo and L. Mendoza-Cadena. \textit{On Mixed Cages of girth 6}, arXiv:2401.14768v2. In particular, if $q$ is an even prime power w…

Solution to a problem on isolation of $3$-vertex paths
Karl Bartolo, Peter Borg, Dayle Scicluna
https://arxiv.org/abs/2506.19149 https://

Solution to a problem on isolation of $3$-vertex paths
The $3$-path isolation number of a connected $n$-vertex graph $G$, denoted by $ι(G,P_3)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects each $3$-vertex path of $G$, meaning that no two edges of $G-N[D]$ intersect. Zhang and Wu proved that $ι(G,P_3) \leq 2n/7$ unless $G$ is a $3$-path or a $3$-cycle or a $6$-cycle. The bound is attained by infinitely many graphs having induced $6$-cycles. Huang, Zhang and Jin pr…

Labeled Chip-Firing on Directed $k$-ary Trees and Where Chips Land
Ryota Inagaki, Tanya Khovanova, Austin Luo
https://arxiv.org/abs/2506.20656 https://

Labeled Chip-Firing on Directed $k$-ary Trees and Where Chips Land
Chip-firing is a combinatorial game played on a graph, in which chips are placed and dispersed on the vertices until a stable configuration is achieved. We study a chip-firing variant on an infinite, rooted directed $k$-ary tree, where we place $k^n$ chips labeled $1,2,3,\dots, k^n$ on the root for some nonnegative integer $n$. A vertex $v$ can fire if it has at least $k$ chips; when it fires, $k$ chips are selected, and the chip with the $i$th smallest label is sent to the $i$th leftmost child…

as_skitter: Skitter IP graph (2005)
An aggregate snapshot of the Internet Protocol (IP) graph, as measured by the traceroute tool on CAIDA's skitter infrastructure, in 2005.
This network has 1696415 nodes and 11095298 edges.
Tags: Technological, Communication, Unweighted
https://networks.skewed.de/net/as_s…

Minors of non-hamiltonian polyhedra and the Herschel family
On-Hei Solomon Lo, Kenta Ozeki
https://arxiv.org/abs/2506.20086 https://a…

Minors of non-hamiltonian polyhedra and the Herschel family
We show that every non-hamiltonian polyhedron contains the Herschel graph as a minor. As an application, we provide a characterization of non-hamiltonian polyhedra without $K_{2,6}$ minors, thereby resolving a conjecture by Ellingham, Marshall, Ozeki, Royle, and Tsuchiya.

Word-Representable Graphs and Locality of Words
Philipp B\"oll, Pamela Fleischmann, Annika Huch, Jana Krei{\ss}, Tim L\"ock, Kajus Park, Max Wiedenh\"oft
https://arxiv.org/abs/2506.19493

Word-Representable Graphs and Locality of Words
In this work, we investigate the relationship between $k$-repre\-sentable graphs and graphs representable by $k$-local words. In particular, we show that every graph representable by a $k$-local word is $(k+1)$-representable. A previous result about graphs represented by $1$-local words is revisited with new insights. Moreover, we investigate both classes of graphs w.r.t. hereditary and in particular the speed as a measure. We prove that the latter ones belong to the factorial layer and that th…

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[1/1]:
- On Graph Odd Edge-Colorings and Odd Edge-Coverings
Xiao-Chuan Liu, Mirko Petru\v{s}evski, Xu Yang

Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
Huye Chen, Jingjian Li, Hao Yu
https://arxiv.org/abs/2506.19888 https://arxi…

Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
After a long term efforts, the Hamiltonian problem of connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally finshed in 2021, see [10]. Fifteen years ago, mathematicians began to challenge this problem for graphs of order $2pq$. Among of them, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p\neq7$ is a prime) contains a Hamilton path, with the exception of a family of graphs which was recently confirmed i…

Complete polyhedral description of chemical graphs of maximum degree at most 3
Valentin Dusollier, S\'ebastien Bonte, Gauvain Devillez, Alain Hertz, Hadrien M\'elot, David Schindl
https://arxiv.org/abs/2506.19768

Complete polyhedral description of chemical graphs of maximum degree at most 3
Chemical graphs are simple undirected connected graphs, where vertices represent atoms in a molecule and edges represent chemical bonds. A degree-based topological index is a molecular descriptor used to study specific physicochemical properties of molecules. Such an index is computed from the sum of the weights of the edges of a chemical graph, each edge having a weight defined by a formula that depends only on the degrees of its endpoints. Given any degree-based topological index and given tw…

What is and is not inside a Cayley graph?
Kolja Knauer, Alvaro Soto Gomez
https://arxiv.org/abs/2506.14088 https://arxiv.org/pdf/2506…

What is and is not inside a Cayley graph?
In this note we show that there is a cubic graph of girth $5$ that is not a subgraph of any minimal Cayley graph. On the other hand, we show that any Generalized Petersen Graph $G(n,k)$ with $\gcd(n,k)=1$ is an induced subgraph of a minimal Cayley graph. These results give insights into two comments of László Babai in [L. Babai, \emph{Automorphism groups, isomorphism, reconstruction}. Graham, R. L. (ed.) et al., Handbook of combinatorics. Vol. 1-2, 1994].

Antimagic labelings of a complete graph
Dr A. N. Bhavale
https://arxiv.org/abs/2506.15221 https://arxiv.org/pdf/2506.15221

Antimagic labelings of a complete graph
In $1990$, Hartsfield and Ringel introduced antimagic graphs. Hartsfield and Ringel conjectured that every connected graph (and in particular, a tree) except $K_2$ is antimagic. In $2010$, Hefetz et al.\ raised two questions: Is every orientation of any simple connected undirected graph antimagic? and Given any undirected graph $G$, does there exist an orientation of $G$ which is antimagic? They call such an orientation an {\it antimagic orientation} of $G$. Recently, Bhavale provided an edge l…

Transparent Rectangle Visibility Graphs
Chaipattana Juntarapomdach, Teeradej Kittipassorn
https://arxiv.org/abs/2506.14522 https://ar…

Transparent Rectangle Visibility Graphs
A transparent rectangle visibility graph (TRVG) is a graph whose vertices can be represented by a collection of non-overlapping rectangles in the plane whose sides are parallel to the axes such that two vertices are adjacent if and only if there is a horizontal or vertical line intersecting the interiors of their rectangles. We show that every threshold graph, tree, cycle, rectangular grid graph, triangular grid graph and hexagonal grid graph is a TRVG. We also obtain a maximum number of edge…

Inverse eigenvalue problem for discrete Schr\"odinger operators of a graph
Anzila Laikhuram, Jephian C. -H. Lin
https://arxiv.org/abs/2506.15430 https…

Inverse eigenvalue problem for discrete Schrödinger operators of a graph
A discrete Schrödinger operator of a graph $G$ is a real symmetric matrix whose $i,j$-entry, $i \neq j$, is negative if $\{i,j\}$ is an edge and zero if it is not an edge, while diagonal entries can be any real numbers. The discrete Schrödinger operators have been used to study vibration theory and the Colin de Verdière parameter. The inverse eigenvalue problem for discrete Schrödinger operators of a graph aims to characterize the possible spectra among discrete Schrödinger operators of a …

Is it easy to regularize a hypergraph with easy links?
Lior Gishboliner, Asaf Shapira, Yuval Wigderson
https://arxiv.org/abs/2506.15582 https://

Is it easy to regularize a hypergraph with easy links?
A partition of a (hyper)graph is $\varepsilon$-homogenous if the edge densities between almost all clusters are either at most $\varepsilon$ or at least $1-\varepsilon$. Suppose a $3$-graph has the property that the link of every vertex has an $\varepsilon$-homogenous partition of size $\text{poly}(1/\varepsilon)$. Does this guarantee that the $3$-graph also has a small homogenous partition? Terry and Wolf proved that such a $3$-graph has an $\varepsilon$-homogenous partition of size given by a…