Acyclic chromatic indices of planar graphs with girth at least five

Authors:
Qiaojun Shu;Weifan Wang
Affiliations:
Department of Mathematics, Zhejiang Normal University, Zhejiang, China 321004;Department of Mathematics, Zhejiang Normal University, Zhejiang, China 321004
Venue:
Journal of Combinatorial Optimization
Year:
2012

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Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a驴(G) of G is the smallest integer k such that G has an acyclic edge coloring using k colors. In this paper, we prove that every planar graph G with girth g(G)驴5 and maximum degree Δ驴12 has a驴(G)=Δ.