Note: Improved bounds for acyclic chromatic index of planar graphs

Authors:
Jianfeng Hou;Guizhen Liu;Guanghui Wang
Affiliations:
Center for Discrete Mathematics, Fuzhou University, Fujian 350002, PR China;School of Mathematics, Shandong University, Jinan 250100, PR China;School of Mathematics, Shandong University, Jinan 250100, PR China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Acyclic coloring problem is a specialized problem that arises in the efficient computation of Hessians. A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by @g"a^'(G), is the least number of colors in an acyclic edge coloring of G. Let G be planar graphs with girth g and maximum degree @D. In this paper, it is shown that if g=4 and @D=8, then @g"a^'(G)@?@D+3; if g=5 and @D=10 or g=6 and @D=6, then @g"a^'(G)=@D.