# Acyclic edge colourings of graphs with large girth

@article{Cai2017AcyclicEC,
title={Acyclic edge colourings of graphs with large girth},
author={Xing Shi Cai and Guillem Perarnau and Bruce A. Reed and Adam Bene Watts},
journal={ArXiv},
year={2017},
volume={abs/1411.3047}
}
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 $\varepsilon>0$, there exists a $g=g(\varepsilon)$ such that if $G$ has girth at least $g$ then $G$ admits an acyclic edge colouring with at most $(1+\varepsilon)\Delta$ colours.
7 Citations

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