Basavaraju, Manu and Chandran, Sunil L (2009) Acyclic Edge Coloring of Graphs with Maximum Degree 4. In: Journal Of Graph Theory, 61 (3). pp. 192-209.
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An 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 is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to John Wiley and Sons.|
|Keywords:||Acyclic edge coloring;acyclic edge chromatic number.|
|Department/Centre:||Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)|
|Date Deposited:||09 Jul 2009 04:46|
|Last Modified:||19 Sep 2010 05:37|
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