Borodin-Kostochka Conjecture holds for odd-hole-free graphs

TL;DR

This paper proves the Borodin-Kostochka Conjecture for a specific class of graphs called odd-hole-free graphs, confirming the conjecture's validity in this case.

Contribution

The paper establishes the truth of the Borodin-Kostochka Conjecture for odd-hole-free graphs, a significant class in graph theory.

Findings

Borodin-Kostochka Conjecture holds for odd-hole-free graphs

Confirmed the conjecture for graphs with maximum degree at least 9

Provides new insights into coloring properties of odd-hole-free graphs

Abstract

The Borodin-Kostochka Conjecture states that for a graph $G$, if $\Delta(G)\geq 9$, then $\chi(G)\leq\max\{\Delta(G)-1,\omega(G)\}$. In this paper, we prove the Borodin-Kostochka Conjecture holding for odd-hole-free graphs.