Year: 2014
Type: preprint
Abstract: We prove bounds on the chromatic number $χ$ of a vertex-transitive graph in terms of its clique number $ω$ and maximum degree $Δ$. We conjecture that every vertex-transitive graph satisfies $χ\le \max \left\{ω, \left\lceil\frac{5Δ+ 3}{6}\right\rceil\right\}$ and we prove results supporting this conjecture. Finally, for vertex-transitive graphs with $Δ\ge 13$ we prove the Borodin-Kostochka conjecture, i.e., $χ\le\max\{ω,Δ-1\}$.
Source: arXiv (Cornell University)
Authors: Cranston, Daniel W., Rabern, Landon
Institution: Virginia Commonwealth University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951941056