McGill University, Montreal
Acyclic edge colourings of graphs with large girth
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 ε > 0 there exists a g = g(ε) such that if G has maximum degree D and girth at least g then it admits an acyclic edge colouring with at most (1 + ε)D colours. This is a joint work with X. S. Cai, B. Reed and A. B. Watts.