Acyclic edge colourings of graphs with large girth. Issue 4 (3rd November 2016) - Cai, X. S.; Perarnau, G.; Reed, B.; Watts, A. B.
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 ε > 0, there exists a g = g ( ε ) such that if G has maximum degree Δ and girth at least g then G admits an acyclic edge colouring with ( 1 + ε ) Δ + O ( 1 ) colours. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 511–533, 2017