A new bound on the acyclic edge chromatic index

Abstract

In this note we obtain a new bound for the acyclic edge chromatic number a ′ (G) of a graph G with maximum degree ∆ proving that a ′ (G) ≤ 3.569(∆ − 1). To get this result we revisit and slightly modify the method described in [Giotis, Kirousis, Psaromiligkos and Thilikos, Theoretical Computer Science, 66: 40-50, 2017].

Moser-Tardos resampling algorithm, entropy compression method and the subset gas

“…In the very specific and singular case of acyclic edge coloring, the Moser-Tardos modified algorithm presented in this paper is able to further slightly improve the bound obtained in [25], and this latter issue is the subject of a separate paper [22]. The rest of the paper is organized as follows.…”