Algebraic proof of Brooks' theorem

TL;DR

This paper provides an algebraic proof of Brooks' theorem and its extension to list coloring, demonstrating the theorem's validity in a broader game coloring context using the Alon-Tarsi method.

Contribution

It introduces an algebraic proof approach for Brooks' theorem and extends its applicability to game coloring scenarios.

Findings

Brooks' theorem holds in a more general game coloring setting.

Algebraic methods can be effectively used to prove graph coloring theorems.

The proof extends the classical theorem to list coloring and game coloring contexts.

Abstract

We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.