Dirac's theorem on chordal graphs implies Brooks' theorem

TL;DR

This paper presents a new proof of the list-color version of Brooks' theorem using Dirac's theorem on chordal graphs, offering an alternative perspective on a classical graph coloring result.

Contribution

It introduces a novel proof technique connecting Dirac's theorem on chordal graphs to Brooks' theorem in list coloring.

Findings

New proof of list-color Brooks' theorem

Connection between Dirac's theorem and Brooks' theorem

Alternative approach to graph coloring proofs

Abstract

We give yet another proof of the list-color version of Brooks' theorem that is due, independently, to Vizing and to Erd\H{o}s, Rubin and Taylor, via a famous theorem of Dirac on chordal graphs.