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Acyclic 4-choosability of Planar Graphs with Girth at Least 5

  • Mickaël Montassier
Part of the Trends in Mathematics book series (TM)

Abstract

A proper vertex coloring of a graph G = (V,E) is acyclic if G contains no bicolored cycle. A graph G is L-list colorable, for a given list assignment L = L(v): vV, if there exists a proper coloring c of G such that c(v) ∈ L(v) for all vV . If G is L-list colorable for every list assignment with |L(v)| ≥ κ for all vV, then G is called κ-choosable. A graph is said to be acyclically κ-choosable if these L-list colorings can be chosen to be acyclic. In this paper, we prove that if G is planar with girth g ≥ 5, then G is acyclically 4-choosable. This improves the result of Borodin, Kostochka and Woodall [[BKW99]] concerning the acyclic chromatic number of planar graphs with girth at least 5.

Keywords

Planar Graph Proper Color Connected Planar Graph Minimum Counterexample Large Girth 
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

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Mickaël Montassier
    • 1
  1. 1.LaBRI UMR CNRS 5800Université Bordeaux 1Talence CedexFrance

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