Coloring claw-free graphs with \Delta-1 colors

TL;DR

This paper proves that all claw-free graphs without large cliques can be colored with one fewer than their maximum degree, advancing understanding of graph coloring in specific graph classes.

Contribution

It establishes a new coloring bound for claw-free graphs lacking large cliques, extending previous results in graph coloring theory.

Findings

Claw-free graphs without large cliques are ( ext{Delta}-1)-colorable.

The result applies to graphs with maximum degree at least 9.

This advances the theory of graph coloring in restricted graph classes.

Abstract

We prove that every claw-free graph $G$ that doesn't contain a clique on $\Delta(G) \geq 9$ vertices can be $\Delta(G) - 1$ colored.