The fractional chromatic number of triangle-free subcubic graphs

TL;DR

This paper proves that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11, improving previous bounds and confirming a conjecture for this class of graphs.

Contribution

The authors establish a tighter upper bound of 32/11 for the fractional chromatic number of triangle-free subcubic graphs, advancing the understanding of graph coloring.

Findings

Fractional chromatic number of such graphs is at most 32/11

Improves previous bounds from estimates of Hatami, Zhu, Lu, and Peng

Confirms a conjecture by Heckman and Thomas

Abstract

Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 (which is roughly 2.909).