Tootfinder

On cubic vertex-transitive graphs of given girth
Ted Dobson, Ademir Hujdurovi\'c, Wilfried Imrich, Ronald Ortner
https://arxiv.org/abs/2507.05821 https…

On cubic vertex-transitive graphs of given girth
A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth alm…

us_roads: United States roads (2000)
The road networks of the 50 US States and the District of Columbia based on UA Census 2000 TIGER/Line Files. Edges are stretches of road and vertices are intersections of roads. The data sets were assembled by Dominik Schultes. The 'merged' network contains all the states merged together.
This network has 540981 nodes and 664215 edges.
Tags: Transportation, Roads, Unweighted

Omroep Flevoland - Nieuws - Bewoners komen in actie: 'Oudste weg van Lelystad mag niet verdwijnen'
https://www.omroepflevoland.nl/nieuws/436878/bewoners-komen-in-actie-oudste-weg-van-lelystad-mag-niet-verdwijnen

Squares, three fleas, sporadic integer sets, and squares
Giedrius Alkauskas
https://arxiv.org/abs/2508.05347 https://arxiv.org/pdf/2508.05347

Squares, three fleas, sporadic integer sets, and squares
In the plane, three integer points ("fleas") are given. At every tick of time, two of them (say, P,Q) instantly jump to two vacant points R,S, so that PQRS is a square with that order of vertices. Description of all integers and half-integers which occur as areas of spanned triangles turns out to be unexpectedly intricate problem. For example, if one starts from a triple (0,0), (2,0), (4,1), these positive integers are missed: 2*{0, 1, 4, 15, 16, 20, 79, 84, 95, 119, 156}, with no other up to 3…

Parametric Analysis of First High-Gain Vertical Fe-doped Ultrafast Ga2O3 Photoconductive Semiconductor Switch
N. Karpourazar, S. K. Mazumder, V. Jangir, K. M. Dowling, J. Leach, L. Voss
https://arxiv.org/abs/2508.04911

Parametric Analysis of First High-Gain Vertical Fe-doped Ultrafast Ga2O3 Photoconductive Semiconductor Switch
We investigate, as part of a Lawrence-Livermore-National-Laboratory (LLNL) sponsored-research work initiated in February of 2021, the parametric performance analysis of ultra-wide bandgap (UWBG) Fe-doped Ga2O3 photoconductive semiconductor switch (FG-PCSS) with embedded electrode. The detailed SILVACO based simulation of the FG-PCSS uses experimentally obtained lifetime, absorption coefficient, and mobility data. The key analysis results, demonstrated first to the sponsor LLNL in 2022, focus on…

PE firm TPG completes its $7.6B acquisition of the remaining 70% stake in DirecTV from AT&T, marking AT&T's exit from media (Dan Primack/Axios)
https://www.axios.com/2025/07/07/att-directv-tpg

AT&T completes $7.6 billion sale of DirecTV
Buying a media company in the name of vertical synergies rarely ends well.

Online Sparsification of Bipartite-Like Clusters in Graphs
Joyentanuj Das, Suranjan De, He Sun
https://arxiv.org/abs/2508.05437 https://arxiv.org/pdf/2508.…

Online Sparsification of Bipartite-Like Clusters in Graphs
Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low conductance, a sequence of recent studies highlights the importance of the inter-connection between vertex sets when analysing real-world datasets. Following this line of research, in this work we study bipartite-like clusters and present efficient and onlin…

Short rainbow cycles for families of small edge sets
He Guo
https://arxiv.org/abs/2507.04581 https://arxiv.org/pdf/2507.04581

Short rainbow cycles for families of small edge sets
In 2019, Aharoni proposed a conjecture generalizing the Caceetta-Häggkvist conjecture: if an $n$-vertex graph $G$ admits an edge coloring (not necessarily proper) with $n$ colors such that each color class has size at least $r$, then $G$ contains a rainbow cycle of length at most $\lceil n/r\rceil$. Recent works \cite{AG2023,ABCGZ2023,G2025} have shown that if a constant fraction of the color classes are non-star, then the rainbow girth is $O(\log n)$. In this note, we extend these results, an…

HiPerMotif: Novel Parallel Subgraph Isomorphism in Large-Scale Property Graphs
Mohammad Dindoost, Oliver Alvarado Rodriguez, Bartosz Bryg, Ioannis Koutis, David A. Bader
https://arxiv.org/abs/2507.04130

HiPerMotif: Novel Parallel Subgraph Isomorphism in Large-Scale Property Graphs
Subgraph isomorphism, essential for pattern detection in large-scale graphs, faces scalability challenges in attribute-rich property graphs used in neuroscience, systems biology, and social network analysis. Traditional algorithms explore search spaces vertex-by-vertex from empty mappings, leading to extensive early-stage exploration with limited pruning opportunities. We introduce HiPerMotif, a novel hybrid parallel algorithm that fundamentally shifts the search initialization strategy. After …

Space-Efficient Hierholzer: Eulerian Cycles in O(m) Time and O(n) Space
Ziad Ismaili Alaoui, Detlef Plump, Sebastian Wild
https://arxiv.org/abs/2508.05251 https://

Space-Efficient Hierholzer: Eulerian Cycles in O(m) Time and O(n) Space
We describe a simple variant of Hierholzer's algorithm that finds an Eulerian cycle in a (multi)graph with $n$ vertices and $m$ edges using $\mathrm{O}(n \lg m)$ bits of working memory. This substantially improves the working space compared to standard implementations of Hierholzer's algorithm, which use $\mathrm{O}(m \lg n)$ bits of space. Our algorithm runs in linear time, like the classical versions, but avoids an $\mathrm{O}(m)$-size stack of vertices or storing information for each edge. T…