Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

D. Fan, S. Goryainov, X. Huang, H. Lin, The spanning k-trees, perfect matchings and spectral radius of graphs, Linear Multilinear Algebra 70 (2022), 7264–7275. P ...

Power graphs provide an innovative way to visualise and analyse the algebraic structure of finite groups. In a power graph, the elements of a finite group serve as vertices, and an edge is drawn ...

We call a rational map f graph critical if any critical point either belongs to an invariant finite graph G, or has minimal limit set, or is nonrecurrent and has limit set disjoint from G. We prove ...

On March 15, intriguing seminar announcements sent rumblings through the field of combinatorics, the mathematical study of counting. Three collaborators planned to give coordinated talks the following ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...