Subcubic triangle-free graphs have fractional chromatic number at most 14/5

TL;DR

This paper proves that all subcubic triangle-free graphs have a fractional chromatic number at most 14/5, confirming a longstanding conjecture and advancing understanding of graph coloring properties.

Contribution

It provides a new proof that subcubic triangle-free graphs have fractional chromatic number at most 14/5, resolving a conjecture by Heckman and Thomas.

Findings

Confirmed the fractional chromatic number bound of 14/5 for subcubic triangle-free graphs

Provided a new proof of a known conjecture in graph theory

Strengthened the theoretical understanding of graph coloring constraints

Abstract

We prove that every subcubic triangle-free graph has fractional chromatic number at most 14/5, thus confirming a conjecture of Heckman and Thomas [A new proof of the independence ratio of triangle-free cubic graphs. Discrete Math. 233 (2001), 233--237].