Acyclic edge colourings of graphs with large girth

This is the peer reviewed version of the following article: Cai, X. S., Perarnau, G. , Reed, B. and Watts, A. B. (2017), Acyclic edge colourings of graphs with large girth. Random Struct. Alg., 50: 511-533. doi:10.1002/rsa.20695, which has been published in final form at https://doi.org/10.1002/rsa.20695. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsAn 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 e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least g then G admits an acyclic edge colouring with (1 + e)¿+O(1) colours.Postprint (author's final draft

Acyclic edge coloring of subcubic graphs

AbstractAn acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors

Acyclic edge colourings of graphs with large girth

This is the peer reviewed version of the following article: Cai, X. S., Perarnau, G. , Reed, B. and Watts, A. B. (2017), Acyclic edge colourings of graphs with large girth. Random Struct. Alg., 50: 511-533. doi:10.1002/rsa.20695, which has been published in final form at https://doi.org/10.1002/rsa.20695. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsAn 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 e > 0, there exists a g = g(e) such that if G has maximum degree ¿ and girth at least g then G admits an acyclic edge colouring with (1 + e)¿+O(1) colours