Tootfinder

Edge open packing: further characterizations
Arti Pandey, Kamal Santra
https://arxiv.org/abs/2508.01935 https://arxiv.org/pdf/2508.01935

Edge open packing: further characterizations
Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\in E(G)$ are said to have \emph{common edge} $e\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an endpoint of $e_2$ in $G$. A subset $D\subseteq E(G)$ is called an \emph{edge open packing set} in $G$ if no two edges in $D$ share a common edge in $G$, and the largest size of such a set in $G$ is known as \emph{edge open packing number}, represented by $ρ_{e}^o(G)…

Replaced article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- TGLib: An Open-Source Library for Temporal Graph Analysis
Lutz Oettershagen, Petra Mutzel

This https://arxiv.org/abs/2502.07975 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Sink equilibria and the attractors of learning in games
Characterizing the limit behavior -- that is, the attractors -- of learning dynamics is one of the most fundamental open questions in game theory. In recent work in this front, it was conjectured that the attractors of the replicator dynamic are in one-to-one correspondence with the sink equilibria of the game -- the sink strongly connected components of a game's preference graph -- , and it was established that they do stand in at least one-to-many correspondence with them. We make threefold p…

This https://arxiv.org/abs/2403.03013 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The clique chromatic number of sparse random graphs
The clique chromatic number of a graph is the smallest number of colors in a vertex coloring so that no maximal clique is monochromatic. In this paper, we determine the order of magnitude of the clique chromatic number of the random graph G_{n,p} for most edge-probabilities p in the range n^{-2/5} \ll p \ll 1. This resolves open problems and questions of Lichev, Mitsche and Warnke as well as Alon and Krievelevich. One major proof difficulty stems from high-degree vertices, which prevent maxim…

MRpro - open PyTorch-based MR reconstruction and processing package
Felix Frederik Zimmermann, Patrick Schuenke, Christoph S. Aigner, Bill A. Bernhardt, Mara Guastini, Johannes Hammacher, Noah Jaitner, Andreas Kofler, Leonid Lunin, Stefan Martin, Catarina Redshaw Kranich, Jakob Schattenfroh, David Schote, Yanglei Wu, Christoph Kolbitsch
https://

MRpro - open PyTorch-based MR reconstruction and processing package
We introduce MRpro, an open-source image reconstruction package built upon PyTorch and open data formats. The framework comprises three main areas. First, it provides unified data structures for the consistent manipulation of MR datasets and their associated metadata (e.g., k-space trajectories). Second, it offers a library of composable operators, proximable functionals, and optimization algorithms, including a unified Fourier operator for all common trajectories and an extended phase graph si…

Threshold-Driven Streaming Graph: Expansion and Rumor Spreading
Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, Isabella Ziccardi
https://arxiv.org/abs/2507.23533

Threshold-Driven Streaming Graph: Expansion and Rumor Spreading
A randomized distributed algorithm called RAES was introduced in [Becchetti et al., SODA 2020] to extract a bounded-degree expander from a dense $n$-vertex expander graph $G = (V, E)$. The algorithm relies on a simple threshold-based procedure. A key assumption in [Becchetti et al., SODA 2020] is that the input graph $G$ is static - i.e., both its vertex set $V$ and edge set $E$ remain unchanged throughout the process - while the analysis of RAES in dynamic models is left as a major open questi…

DIY-MKG: An LLM-Based Polyglot Language Learning System
Kenan Tang, Yanhong Li, Yao Qin
https://arxiv.org/abs/2507.01872 https://arxi…

DIY-MKG: An LLM-Based Polyglot Language Learning System
Existing language learning tools, even those powered by Large Language Models (LLMs), often lack support for polyglot learners to build linguistic connections across vocabularies in multiple languages, provide limited customization for individual learning paces or needs, and suffer from detrimental cognitive offloading. To address these limitations, we design Do-It-Yourself Multilingual Knowledge Graph (DIY-MKG), an open-source system that supports polyglot language learning. DIY-MKG allows the…

Extension Decisions in Open Source Software Ecosystem
Elmira Onagh, Maleknaz Nayebi
https://arxiv.org/abs/2507.23168 https://arxiv.org/pdf/2507.23168

Extension Decisions in Open Source Software Ecosystem
GitHub Marketplace is expanding by approximately 41% annually, with new tools; however, many additions replicate existing functionality. We study this phenomenon in the platform's largest segment, Continuous Integration (CI), by linking 6,983 CI Actions to 3,869 providers and mining their version histories. Our graph model timestamps every functionality's debut, tracks its adoption, and clusters redundant tools. We find that approximately 65% of new CI Actions replicate existing capabilities, t…

The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture
Francesco Barioli, Shaun M. Fallat, Himanshu Gupta, Zhongshan Li
https://arxiv.org/abs/2505.24577

The Weak Version of the Graph Complement Conjecture and Partial Results for the Delta Conjecture
Since the transformative workshop by the American Institute of Mathematics on the minimum rank of a graph, two longstanding open problems have captivated the community interested in the minimum rank of graphs: the graph complement conjecture and the $δ$-conjecture. In this paper, we use a classical result of Mader (1972) to establish a weak version of the graph complement conjecture for all key minimum rank parameters. In addition, again using the same result of Mader, we present some extremal…

You are an expert in ontologies and kn owledge graphs? You have an interest (or even better expertise) in materials science engineering? Then you should apply! Open PostDoc/Senior Researcher position at FIZ Karlsruhe ISE Research Team in the Knowledge Graph department. More info at https://www.fiz-k…

LLMs Between the Nodes: Community Discovery Beyond Vectors
Ekta Gujral, Apurva Sinha
https://arxiv.org/abs/2507.22955 https://arxiv.org/pdf/2507.22955

LLMs Between the Nodes: Community Discovery Beyond Vectors
Community detection in social network graphs plays a vital role in uncovering group dynamics, influence pathways, and the spread of information. Traditional methods focus primarily on graph structural properties, but recent advancements in Large Language Models (LLMs) open up new avenues for integrating semantic and contextual information into this task. In this paper, we present a detailed investigation into how various LLM-based approaches perform in identifying communities within social grap…

Is SHACL Suitable for Data Quality Assessment?
Carolina Cort\'es Lasalle, Lisa Ehrlinger, Lorena Etcheverry, Felix Naumann
https://arxiv.org/abs/2507.22305 https://

Is SHACL Suitable for Data Quality Assessment?
Knowledge graphs have been widely adopted in both enterprises, such as the Google Knowledge Graph, and open platforms like Wikidata to represent domain knowledge and support analysis with artificial intelligence. They model real-world information as nodes and edges. To embrace flexibility, knowledge graphs often lack enforced schemas (i.e., ontologies), leading to potential data quality issues, such as semantically overlapping nodes. Therefore, ensuring their quality is essential, as issues in …

On Measuring Long-Range Interactions in Graph Neural Networks
Jacob Bamberger, Benjamin Gutteridge, Scott le Roux, Michael M. Bronstein, Xiaowen Dong
https://arxiv.org/abs/2506.05971

On Measuring Long-Range Interactions in Graph Neural Networks
Long-range graph tasks -- those dependent on interactions between distant nodes -- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize …

$C_4$-free subgraphs of high degree with geometric applications
Zach Hunter, Aleksa Milojevi\'c, Istvan Tomon, Benny Sudakov
https://arxiv.org/abs/2506.23942

$C_4$-free subgraphs of high degree with geometric applications
The Zarankiewicz problem, a cornerstone problem in extremal graph theory, asks for the maximum number of edges in an $n$-vertex graph that does not contain the complete bipartite graph $K_{s,s}$. While the problem remains widely open in the case of general graphs, the past two decades have seen significant progress on this problem for various restricted graph classes -- particularly those arising from geometric settings -- leading to a deeper understanding of their structure. In this paper, w…

The Verge’s open graph description savagely drags Death Stranding with “Hideo Kojima’s Death Stranding is being turned into a video game.” 🤣
I should give the game another shot, but 2 hours of “cinematic” at the start is too much for this old man.

This https://arxiv.org/abs/2410.04394 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A combinatorial approach to nonlinear spectral gaps
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete Poincaré inequality for scalar functions, also satisfies an analogous inequality for functions taking values in \textit{any} normed space with non-trivial cotype. Motivated by applications, it is also greatly important to quantify the dependence of the corresponding optimal Poincaré constant on the cotype $q$. Works of Odell--Schlumprecht (1994), Ozawa (2004), and …

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
Randy Davila, Boris Brimkov, Ryan Pepper
https://arxiv.org/abs/2507.17780 https://

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through yea…

Barrier Method for Inequality Constrained Factor Graph Optimization with Application to Model Predictive Control
Anas Abdelkarim, Holger Voos, Daniel G\"orges
https://arxiv.org/abs/2506.14341

Barrier Method for Inequality Constrained Factor Graph Optimization with Application to Model Predictive Control
Factor graphs have demonstrated remarkable efficiency for robotic perception tasks, particularly in localization and mapping applications. However, their application to optimal control problems -- especially Model Predictive Control (MPC) -- has remained limited due to fundamental challenges in constraint handling. This paper presents a novel integration of the Barrier Interior Point Method (BIPM) with factor graphs, implemented as an open-source extension to the widely adopted g2o framework. O…

On the Conjecture of the Representation Number of Bipartite Graphs
Khyodeno Mozhui, K. V. Krishna
https://arxiv.org/abs/2506.01057 https://

On the Conjecture of the Representation Number of Bipartite Graphs
While the problem of determining the representation number of an arbitrary word-representable graph is NP-hard, this problem is open even for bipartite graphs. The representation numbers are known for certain bipartite graphs including all the graphs with at most nine vertices. For bipartite graphs with partite sets of sizes $m$ and $n$, Glen et al. conjectured that the representation number is at most $\lceil \frac{m+n}{4}\rceil$, where $m+n \ge 9$. In this paper, we show that every bipartit…

Graph quandles: Generalized Cayley graphs of racks and right quasigroups
Luc Ta
https://arxiv.org/abs/2506.04437 https://arxiv.org/pd…

Graph quandles: Generalized Cayley graphs of racks and right quasigroups
We solve two open problems of Valeriy Bardakov about Cayley graphs of racks and graph-theoretic realizations of right quasigroups. We also extend Didier Caucal's classification of labeled Cayley digraphs to right quasigroups and related algebraic structures like quandles. First, we characterize markings of graphs that realize racks. As an application, we construct rack-theoretic (di)graph invariants from permutation representations of graph automorphism groups. We describe how to compute thes…

Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection
Vijay K. Dubey (The University of Texas at Austin), Collin E. Haese (The University of Texas at Austin), Osman G\"ultekin (The University of Texas at Austin), David Dalton (University of Glasgow), Manuel K. Rausch (The University of Texas at Austin), Jan N. Fuhg (The University of Texas at Austin)

Graph Neural Network Surrogates for Contacting Deformable Bodies with Necessary and Sufficient Contact Detection
Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable bodies, especially in the context of varying geometries, is still an open issue. In particular, existing methods are confined to rigid body contact or, at best, contact between rigid and soft objects with well-defined contact planes. Furthermore, they employ c…

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…

Ramsey numbers for 1-degenerate 3-graphs
Peter Allen, Simona Boyadzhiyska, Mat\'ias Pavez-Sign\'e
https://arxiv.org/abs/2507.23623 https://arxiv.or…

Ramsey numbers for 1-degenerate 3-graphs
We construct a 3-uniform 1-degenerate hypergraph on $n$ vertices whose 2-colour Ramsey number is $Ω\big(n^{3/2}/\log n\big)$. This shows that all remaining open cases of the hypergraph Burr-Erdős conjecture are false. Our graph is a variant of the celebrated hedgehog graph. We additionally show near-sharp upper bounds, proving that all 3-uniform generalised hedgehogs have 2-colour Ramsey number $O\big(n^{3/2}\big)$.

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…

Fast automated adjoints for spectral PDE solvers
Calum S. Skene, Keaton J. Burns
https://arxiv.org/abs/2506.14792 https://arxiv.org/p…

Fast automated adjoints for spectral PDE solvers
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic differentiation to symbolic graph representations of PDEs, efficiently constructing adjoint solvers that retain the speed and memory efficiency of this important class of modern numerical methods. This approach enables users to compute gradients and perform optim…

This https://arxiv.org/abs/2506.04437 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graph quandles: Generalized Cayley graphs of racks and right quasigroups
We solve two open problems of Valeriy Bardakov about Cayley graphs of racks and graph-theoretic realizations of right quasigroups. We also extend Didier Caucal's classification of labeled Cayley digraphs to right quasigroups and related algebraic structures like quandles. First, we characterize markings of graphs that realize racks. As an application, we construct rack-theoretic (di)graph invariants from permutation representations of graph automorphism groups. We describe how to compute thes…

BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Qingsong Gu, Hua Qiu
https://arxiv.org/abs/2507.14858 https://

BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Let $K$ be a p.c.f. self-similar set equipped with a strongly recurrent Dirichlet form. Under a homogeneity assumption, for an open set $Ω\subset K$ whose boundary $\partial Ω$ is a graph-directed self-similar set, we prove that the eigenvalue counting function $ρ^Ω(x)$ of the Laplacian with Dirichlet or Neumann boundary conditions (Neumann only for connected $Ω$) has an explicit second term as $x\to +\infty$, beyond the dominant Weyl term. If $\partialΩ$ has a strong iterated structure, …

Sufficient conditions of $k$-leaf-connected graphs and spanning trees with bounded total $k$-excess
Guoyan Ao, Ruifang Liu, Jinjiang Yuan
https://arxiv.org/abs/2507.04400

Sufficient conditions of $k$-leaf-connected graphs and spanning trees with bounded total $k$-excess
Chvátal and Erdös [Discrete Math. 2 (1972) 111-113] stated that, for an $m$-connected graph $G$, if its independence number $α(G)\leq m-1$, then $G$ is Hamilton-connected. Note that $k$-leaf-connectedness is a natural generalization of Hamilton-connectedness of a graph. Ozeki and Yamashita [Graphs Combin. 27 (2011) 1-26] posed an open problem: What is the sufficient condition based on the independence number for an $m$-connected graph to be $k$-leaf-connected? In this paper, we prove that if…

This https://arxiv.org/abs/2505.11205 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

IssueCourier: Multi-Relational Heterogeneous Temporal Graph Neural Network for Open-Source Issue Assignment
Issue assignment plays a critical role in open-source software (OSS) maintenance, which involves recommending the most suitable developers to address the reported issues. Given the high volume of issue reports in large-scale projects, manually assigning issues is tedious and costly. Previous studies have proposed automated issue assignment approaches that primarily focus on modeling issue report textual information, developers' expertise, or interactions between issues and developers based on h…

Sidorenko-Type Inequalities for Even Subdivisions over Finite Abelian Groups
Yuqi Zhao
https://arxiv.org/abs/2507.15723 https://arxiv…

Sidorenko-Type Inequalities for Even Subdivisions over Finite Abelian Groups
Sidorenko's conjecture asserts that every bipartite graph $H$ has the property that, for any host graph $G$, the homomorphism density from $H$ to $G$ is asymptotically at least as large as in a quasirandom graph with the same edge density as $G$. While the conjecture remains still very open, Szegedy showed that it suffices to verify the inequality when the host graph is a Cayley graph over a finite group. In this paper, we prove that Sidorenko's conjecture holds for all even subdivisions of a…

Designing Parallel Algorithms for Community Detection using Arachne
Fuhuan Li, Zhihui Du, David A. Bader
https://arxiv.org/abs/2507.06471 https://

Designing Parallel Algorithms for Community Detection using Arachne
The rise of graph data in various fields calls for efficient and scalable community detection algorithms. In this paper, we present parallel implementations of two widely used algorithms: Label Propagation and Louvain, specifically designed to leverage the capabilities of Arachne which is a Python-accessible, open-source framework for large-scale graph analysis. Our implementations achieve substantial speedups over existing Python-based tools like NetworkX and igraph, which lack efficient paral…

Better Bounds for Semi-Streaming Single-Source Shortest Paths
Sepehr Assadi, Gary Hoppenworth, Janani Sundaresan
https://arxiv.org/abs/2507.17841 https://a…

Better Bounds for Semi-Streaming Single-Source Shortest Paths
In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the problem at hand. Approximating (single-source) shortest paths on undirected graphs is a longstanding open question in this model. In this work, we make progress on this question from both upper and lower bound fronts: We present a simple randomized algorith…

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…

OK, that whole preview is pretty bad. I read here
https://fedi.tips/how-do-i-get-a-link-preview-to-appear-in-my-post-on-mastodon/
that one needs to include Open Graph meta tags.
Maybe this will be my next patch to al-folio ?
https://github.com/alshedivat/al-folio
?

Unavoidable pivot-minors in graphs of large rank-depth
Jungho Ahn, Kevin Hendrey, O-joung Kwon, Sang-il Oum
https://arxiv.org/abs/2507.12697 https://

Unavoidable pivot-minors in graphs of large rank-depth
Shrub-depth and rank-depth are related graph parameters that are dense analogs of tree-depth. We prove that for every positive integer $t$, every graph of sufficiently large rank-depth contains a pivot-minor isomorphic to a path on $t$ vertices or a graph consisting of two disjoint cliques of size $t$ joined by a half graph. This answers an open problem raised by Kwon, McCarty, Oum, and Wollan in 2021.

Suns in triangle-free graphs of large chromatic number
Sepehr Hajebi, Sophie Spirkl
https://arxiv.org/abs/2506.10227 https://arxiv.or…

Suns in triangle-free graphs of large chromatic number
For an integer $t\geq 4$, a $t$-sun is a graph obtained from a $t$-vertex cycle $C$ by adding a degree-one neighbor for each vertex of $C$. Trotignon asked whether every triangle-free graph of sufficiently large chromatic number has an induced subgraph that is a $t$-sun for some $t\geq 4$. This remains open, but we show that every triangle-free graph of chromatic number at least $44$ has an induced subgraph that is either a $t$-sun for some $t\geq 5$, or a $4$-sun with a single degree-one verte…

Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
Songling Shan, Arthur Tanyel
https://arxiv.org/abs/2506.12684 https://arxiv.or…

Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
In 1973, Chvátal conjectured that there exists a constant $t_0$ such that every $t_0$-tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, work has been done to confirm it for several graph classes, including all $F$-free graphs for every 5-vertex linear forest $F$ other than $P_5$ and $2P_2\cup P_1$. In this note, we show that 11-tough $(2P_2 \cup P_1)$-free graphs on at least three vertices are Hamiltonian.

Locating-dominating partitions for some classes of graphs
Florent Foucaud, Paras Vinubhai Maniya, Kaustav Paul, Dinabandhu Pradhan
https://arxiv.org/abs/2506.12933

Locating-dominating partitions for some classes of graphs
A dominating set of a graph $G$ is a set $D \subseteq V(G)$ such that every vertex in $V(G) \setminus D$ is adjacent to at least one vertex in $D$. A set $L\subseteq V(G)$ is a locating set of $G$ if every vertex in $V(G) \setminus L$ has pairwise distinct open neighborhoods in $L$. A set $D\subseteq V(G)$ is a locating-dominating set of $G$ if $D$ is a dominating set and a locating set of $G$. The location-domination number of $G$, denoted by $γ_{LD}(G)$, is the minimum cardinality among all …

This https://arxiv.org/abs/2501.02529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Prime Multiple Missing Graphs
The famous Goldbach conjecture remains open for nearly three centuries. Recently Goldbach graphs are introduced to relate the problem with the literature of Graph Theory. It is shown that the connectedness of the graphs is equivalent to the affirmative answer of the conjecture. Some modified version of the graphs, say, near Goldbach graphs are shown to be Hamiltonian for small number of vertices. In this context, we introduce a class of graphs, namely, prime multiple missing graphs such that ne…