A note on coloring vertex-transitive graphs

Abstract

We prove bounds on the chromatic number χ of a vertex-transitive graph in terms of its clique number ! and maximum degree Δ. We conjecture that every vertex-transitive graph satisfies (formula present), and we prove results support-ing this conjecture. Finally, for vertex-transitive graphs with Δ ≥ 13 we prove the Borodin-Kostochka conjecture, i.e.,(formula present).