Acyclic edge colourings of graphs with large girth

@article{Cai2017AcyclicEC,
  title={Acyclic edge colourings of graphs with large girth},
  author={X. S. Cai and G. Perarnau and B. Reed and A. 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. 
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