The Fractional Chromatic Number of Triangle-free Graphs with $Δ\leq 3$

Details The Fractional Chromatic Number of Triangle-free Graphs with $Δ\leq 3$ The Fractional Chromatic Number of Triangle-free Graphs with $Δ\leq 3$

2010-11-10

arxiv.org/abs/1011.2500v1

Mathematics

Combinatorics

24 pages, 42 figures

Scientific paper

Let $G$ be any triangle-free graph with maximum degree $\Delta\leq 3$. Staton proved that the independence number of $G$ is at least $\frac{5}{14}n$. Heckman and Thomas conjectured that Staton's result can be strengthened into a bound on the fractional chromatic number of $G$, namely $\chi_f(G)\leq \frac{14}{5}$. Recently, Hatami and Zhu proved $\chi_f(G) \leq 3 -{3/64}$. In this paper, we prove $\chi_f(G) \leq 3- \frac{3}{43}$.

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