Acyclic edge colourings of graphs with large girth

Abstract

An edge colouring of a graph $G$ is called acyclic if it is proper and every cycle contains at least three colours. We show that for every $\epsilon >0$, there exists a $g=g(\epsilon )$ such that if $G$ has girth at least $g$ then $G$ admits an acyclic edge colouring with at most $(1+\epsilon )\Delta$ colours.

25 pages

References in corpus (3)

• Acyclic edge-coloring using entropy compression
• The Local Cut Lemma
• New Bounds for the Acyclic Chromatic Index