Yet another proof of Brooks' theorem

TL;DR

This paper presents a new, simplified proof of Brooks' theorem that avoids the common reduction to the cubic case, offering a more straightforward approach.

Contribution

It introduces a novel, simplified proof of Brooks' theorem that bypasses the traditional reduction to cubic graphs.

Findings

Proof is more straightforward and easier to understand

Avoids reduction to cubic graphs entirely

Contributes to the theoretical understanding of graph coloring

Abstract

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.