Note: Acyclic edge coloring of planar graphs with large girth

Authors:
Dongxiao Yu;Jianfeng Hou;Guizhen Liu;Bin Liu;Lan Xu
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong, 250100, PR China;School of Mathematics, Shandong University, Jinan, Shandong, 250100, PR China;School of Mathematics, Shandong University, Jinan, Shandong, 250100, PR China;School of Mathematics, Shandong University, Jinan, Shandong, 250100, PR China;Department of Mathematics, Changji University, Changji, Xinjiang, 831100, PR China
Venue:
Theoretical Computer Science
Year:
2009

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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 edge chromatic number @g"a^'(G) of G is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that @g"a^'(G)@?@D(G)+2. In this paper, we consider the sufficient conditions for the planar graphs satisfying @g"a^'(G)@?@D(G)+1 and @g"a^'(G)=@D(G).