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Acyclic Edge Coloring of Graphs with Maximum Degree 4

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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Abstract

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
URI: http://eprints.iisc.ernet.in/id/eprint/21333

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