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# Acyclic edge coloring of 2-degenerate graphs

Basavaraju, Manu and Chandran, Sunil L (2012) Acyclic edge coloring of 2-degenerate graphs. In: Journal of Graph Theory, 69 (1). pp. 1-27. PDF Acyclic_Edge.pdf - Published Version Restricted to Registered users only Download (286kB) | Request a copy

## 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 Copyright of this article belongs to John Wiley and Sons. acyclic edge coloring;acyclic edge chromatic number; 2-degenerate graphs;series-parallel graphs;outer planar graphs Division of Electrical Sciences > Computer Science & Automation Id for Latest eprints 27 Jan 2012 12:16 27 Jan 2012 12:16 http://eprints.iisc.ac.in/id/eprint/43204 View Item