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Acyclic Edge Coloring of Triangle-Free Planar Graphs

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.

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Official URL: http://dx.doi.org/10.1002/jgt.20651


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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