Brooks' Theorem from the Alon--Tarsi Theorem

Stephen Hartke, UNL


Meeting Time: March 29, 2011, 2:00-2:50pm

Abstract: Brooks' Theorem states that the chromatic number of a graph is bounded by its maximum degree, except for complete graphs and odd cycles. Recently, Hladky, Kral, and Schauz gave a proof of Brooks' Theorem using the Alon--Tarsi Theorem, a powerful theorem that gives coloring results from the Combinatorial Nullstellensatz. We will discuss the Alon--Tarsi Theorem, and present Hladky, Kral, and Schauz's proof of Brooks' Theorem.