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Adjacent vertex-distinguishing edge coloring of graphs

  • Marthe Bonamy
  • Nicolas Bousquet
  • Hervé Hocquard
Part of the CRM Series book series (PSNS, volume 16)

Abstract

An adjacent vertex-distinguishing edge coloring (AVD-coloring) of a graph is a proper edge coloring such that no two neighbors are adjacent to the same set of colors. Zhang et al. [17] conjectured that every connected graph on at least 6 vertices is AVD (Δ + 2)-colorable, where A is the maximum degree. In this paper, we prove that (Δ + 1) colors are enough when A is sufficiently larger than the maximum average degree, denoted mad. We also provide more precise lower bounds for two graph classes: planar graphs, and graphs with mad < 3. In the first case, Δ ≥ 12 suffices, which generalizes the result of Edwards et al. [7] on planar bipartite graphs. No other results are known in the case of planar graphs. In the second case, Δ ≥ 4 is enough, which is optimal and completes the results of Wang and Wang [14] and of Hocquard and Montassier [9].

Keywords

Planar Graph Discrete Math Graph Class Edge Coloring Chromatic Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  • Marthe Bonamy
    • 1
  • Nicolas Bousquet
    • 1
  • Hervé Hocquard
    • 2
  1. 1.LIRMM (Université Montpellier 2)Montpellier CedexFrance
  2. 2.LaBRI (Université Bordeaux 1)Talence CedexFrance

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