Acyclic edge coloring of sparse graphs
Abstract
A proper edge coloring of a graph G is called acyclic if there is no bichromatic cycle in G. The acyclic chromatic index of G, denoted by 'a(G), is the least number of colors k such that G has an acyclic edge k-coloring. The maximum average degree of a graph G, denoted by (G), is the maximum of the average degree of all subgraphs of G. In this paper, it is proved that if (G)<4, then 'a(G)≤(G)+2; if (G)<3, then 'a(G)≤(G)+1. This implies that every triangle-free planar graph G is acyclically edge ((G)+2)-colorable.
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