Basavaraju, Manu and Chandran, Sunil L
(2012)
*Acyclic edge coloring of 2-degenerate graphs.*
In: Journal of Graph Theory, 69
(1).
pp. 1-27.

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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). A graph is called 2-degenerate if any of its induced subgraph has a vertex of degree at most 2. The class of 2-degenerate graphs properly contains seriesparallel graphs, outerplanar graphs, non - regular subcubic graphs, planar graphs of girth at least 6 and circle graphs of girth at least 5 as subclasses. It was conjectured by Alon, Sudakov and Zaks (and much earlier by Fiamcik) that a'(G)<=Delta + 2, where Delta = Delta(G) denotes the maximum degree of the graph. We prove the conjecture for 2-degenerate graphs. In fact we prove a stronger bound: we prove that if G is a 2-degenerate graph with maximum degree ?, then a'(G)<=Delta + 1. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 68:1-27, 2011

Item Type: | Journal Article |
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Related URLs: | |

Additional Information: | Copyright of this article belongs to John Wiley and Sons. |

Keywords: | acyclic edge coloring;acyclic edge chromatic number; 2-degenerate graphs;series-parallel graphs;outer planar graphs |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation) |

Date Deposited: | 27 Jan 2012 12:16 |

Last Modified: | 27 Jan 2012 12:16 |

URI: | http://eprints.iisc.ernet.in/id/eprint/43204 |

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