Some results on acyclic edge coloring of plane graphs

  • Authors:

  • Wei Dong;Baogang Xu

  • Affiliations:

  • School of Mathematical Science, Nanjing Normal University, Nanjing, China, 210097 and School of Mathematics and Information Technology, Nanjing Xiaozhuang College, Nanjing, China, 211171;School of Mathematical Science, Nanjing Normal University, Nanjing, China, 210097

  • Venue:
  • Information Processing Letters
  • Year:
  • 2010

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Abstract

An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. The acyclic chromatic index of a graph G, denoted by @a^'(G), is the minimum number k such that G admits an acyclic edge coloring using k colors. Let G be a plane graph with maximum degree @D and girth g. In this paper, we prove that @a^'(G)=@D(G) if one of the following conditions holds: (1) @D=8 and g=7; (2) @D=6 and g=8; (3) @D=5 and g=9; (4) @D=4 and g=10; (5) @D=3 and g=14. We also improve slightly a result of A. Fiedorowicz et al. (2008) [7] by showing that every triangle-free plane graph admits an acyclic edge coloring using at most @D(G)+5 colors.