Basavaraju, Manu and Chandran, Sunil L
(2012)
*Acyclic Edge Coloring of Triangle-Free Planar Graphs.*
In: JOURNAL OF GRAPH THEORY, 71
(4).
pp. 365-385.

## 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 (and much earlier by Fiamcik) that a'(G) ? ? + 2, where ? = ?(G) denotes the maximum degree of the graph. If every induced subgraph H of G satisfies the condition |E(H)| ? 2|V(H)|-1, we say that the graph G satisfies Property A. In this article, we prove that if G satisfies Property A, then a'(G) ? ? + 3. Triangle-free planar graphs satisfy Property A. We infer that a'(G) ? ? + 3, if G is a triangle-free planar graph. Another class of graph which satisfies Property A is 2-fold graphs (union of two forests). (C) 2011 Wiley Periodicals, Inc. J Graph Theory

Item Type: | Journal Article |
---|---|

Additional Information: | Copyright for this article belongs to WILEY-BLACKWELL, USA |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Depositing User: | Francis Jayakanth |

Date Deposited: | 28 Dec 2012 08:36 |

Last Modified: | 28 Dec 2012 08:36 |

URI: | http://eprints.iisc.ac.in/id/eprint/45461 |

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