The fractional chromatic number of triangle-free subcubic graphs

Abstract

Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 ≈ 2.909.

Bounding the Fractional Chromatic Number of $K_\Delta$-Free Graphs

“…We remark that this lemma is most sensibly applied when X is a clique. 3 The unweighted version is described as folklore in [8] and was used earlier in [11], and probably elsewhere.…”

Subcubic triangle-free graphs have fractional chromatic number at most 14/5

“…There are also two very recent improvements on the upper bound -but with totally different approaches. The first one is due to Ferguson, Kaiser and Král' [7], who showed that the fractional chromatic number is at most 32/11 ≈ 2.909. The other one is due to Liu [16], who improved the upper bound to 43/15 ≈ 2.867.…”

An Upper Bound on the Fractional Chromatic Number of Triangle-Free Subcubic Graphs

“…Lu and Peng [11] improved the bound to χ f (G) ≤ 3 − 3/43 ≈ 2.930. Ferguson, Kaiser and Král' [4] further improved that χ f (G) ≤ 32/11 ≈ 2.909. In this paper, we prove the following theorem.…”