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 514|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)≤145. Recently, Hatami and Zhu proved that χf(G)≤3−364. In this paper, we prove χf(G)≤3−343.