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

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


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.


Planar Graph Proper Color Connected Planar Graph Minimum Counterexample Large Girth 
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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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