Tootfinder

flickr_groups: OSN user groups (2007)
Bipartite networks of the affiliations between users and groups on several online social network sites, including Flickr, YouTube, LiveJournal, and Orkut, extracted in 2007.
This network has 499610 nodes and 8545307 edges.
Tags: Social, Online, Unweighted
https://networ…

A combination theorem for the twist conjecture for Artin groups
Oli Jones, Giorgio Mangioni, Giovanni Sartori
https://arxiv.org/abs/2507.13971 https://

A combination theorem for the twist conjecture for Artin groups
We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the isomorphism problem for Artin groups. Along the way we also prove a combination result for the ribbon property for vertices.

A note on $\chi$-unbounded classes of geometric graphs
Pegah Pournajafi
https://arxiv.org/abs/2507.14884 https://arxiv.org/pdf/2507.1…

A note on $χ$-unbounded classes of geometric graphs
We show that there exist infinitely many classes of intersection graphs of geometric objects that are not $χ$-bounded -- namely, $d$-CBU graphs for $d\geq 3$ -- and each is incomparable with the class of Burling graphs. This answers a folklore open problem on whether Burling graphs are the sole source of unbounded chromatic number among geometric intersection classes.

Three skeptics called war "media lies"—then visited Ukraine's bombed hospitals and mass graves - Euromaidan Press
https://euromaidanpress.com/2025/07/21/three-skeptics-called-war-media-lies-then-visited-ukraines-bombed-hospitals-and-mass-graves/

This whole opinion, while well-meaning and bringing up generally good points (we humans can decide what technology we research and how we use it)—misses the point: there will not be an “AGI” that derives from current “AI” technology.
What the “AI” companies are proposing and the media is accepting at face value is like saying ever more realistic graphics in computer games will suddenly reach some threshold and the graphics will become the real world.
It’s nonsense.
https://www.theguardian.com/commentisfree/ng-interactive/2025/jul/21/human-level-artificial-intelligence

Chinese nation-state groups exploiting SharePoint vulnerability, Microsoft confirms https://therecord.media/microsoft-sharepoint-vulnerabilities-china-groups-exploiting

revolution: American Revolutionary groups (1765-1783)
A bipartite network of the memberships of notable people and organizations, from the American Revolution (1765-1783) between users and groups on YouTube, extracted from a larger YouTube network in 2007.
This network has 141 nodes and 160 edges.
Tags: Social, Affiliation, Unweighted
http…

Asymptotic normality of embedding distributions of some families of graphs
Yichao Chen, Wenjie Fang, Zhicheng Gao, Jinlian Zhang
https://arxiv.org/abs/2507.15751

Asymptotic normality of embedding distributions of some families of graphs
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are often the normal distribution. We establish the asymptotic normality of several families of graphs by developing adapted tools and frameworks. We expect that these tools and frameworks can be used on other families of graphs to establish the asymptotic normali…

Multi-virtual braid groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, Madeti Prabhakar
https://arxiv.org/abs/2507.14551 https://

Multi-virtual braid groups
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. …

Subgroup Perfect Codes of $\mathcal{A}_t$-Groups and Their Applications
Huye chen, Binbin Li, Jingjian Li, Hao Yu
https://arxiv.org/abs/2507.15206 https://…

Subgroup Perfect Codes of $\mathcal{A}_t$-Groups and Their Applications
A subset $C$ of the vertex set of a graph $Γ$ is called a perfect code in $Γ$ if every vertex of $Γ$ is at distance no more than 1 to exactly one vertex of $C$. A subgroup $H$ of a group $G$ is called a subgroup perfect code of $G$ if $H$ is a perfect code in some Cayley graph of $G$. Recently, Zhang reveals that the study of subgroup perfect codes of finite groups naturally reduces to the case of $p$-groups, especially $2$-groups. Based on the combined works of Berkovich, Janko and Zhang, e…