Acyclic chromatic indices of planar graphs with large girth

Authors:
Weifan Wang;Qiaojun Shu;Kan Wang;Ping Wang
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada
Venue:
Discrete Applied Mathematics
Year:
2011

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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^'(G) of G is the smallest 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) and maximum degree @D has a^'(G)=@D if there exists a pair (k,m)@?{(3,11),(4,8),(5,7),(8,6)} such that G satisfies @D=k and g(G)=m.