11/4-colorability of subcubic triangle-free graphs

TL;DR

This paper proves that almost all connected subcubic triangle-free graphs have a fractional chromatic number at most 11/4, improving bounds for planar graphs and identifying exceptions.

Contribution

It establishes a tight bound of 11/4 for the fractional chromatic number of connected subcubic triangle-free graphs, with only two exceptions.

Findings

Most such graphs have fractional chromatic number ≤ 11/4

The bound is tight except for two specific graphs

Improves previous bounds for planar graphs

Abstract

We prove that up to two exceptions, every connected subcubic triangle-free graph has fractional chromatic number at most 11/4. This is tight unless further exceptional graphs are excluded, and improves the known bound on the fractional chromatic number of subcubic triangle-free planar graphs.