The fractional chromatic number of triangle-free graphs with Δ<3

Let G be a triangle-free graph with maximum degree at most 3. Staton proved that the independence number of G is at least 5 14 |V (G)|. Heckman and Thomas conjectured that Staton’s result can be strengthened into a bound on the fractional chromatic number of G, namely χf (G) ≤ 14 5 . Recently, Hatami and Zhu proved that χf (G) ≤ 3 − 3 64 . In this paper, we prove χf (G) ≤ 3 − 3 43 . © 2012 Elsevier B.V. All rights reserved.