The fractional chromatic number of triangle-free graphs with

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 χ f ( G ) ≤ 14 5 . Recently, Hatami and Zhu proved that χ f ( G ) ≤ 3 − 3 64 . In this paper, we prove χ f ( G ) ≤ 3 − 3 43 .