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Journal of Combinatorial Optimization

, Volume 26, Issue 1, pp 152–160 | Cite as

Adjacent vertex-distinguishing edge coloring of graphs with maximum degree Δ

  • Hervé Hocquard
  • Mickaël Montassier
Article

Abstract

An adjacent vertex-distinguishing edge coloring, or avd-coloring, of a graph G is a proper edge coloring of G such that no pair of adjacent vertices meets the same set of colors. Let \(\operatorname {mad}(G)\) and Δ(G) denote the maximum average degree and the maximum degree of a graph G, respectively. In this paper, we prove that every graph G with Δ(G)≥5 and \(\operatorname{mad}(G) < 3-\frac {2}{\Delta}\) can be avd-colored with Δ(G)+1 colors. This completes a result of Wang and Wang (J. Comb. Optim. 19:471–485, 2010).

Keywords

Adjacent vertex-distinguishing edge coloring Maximum average degree 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.LaBRIUniversité Bordeaux ITalence CedexFrance

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