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 |
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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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