Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable

  • Authors:

  • Hervé Hocquard;Mickaël Montassier

  • Affiliations:

  • Université de Bordeaux -- LaBRI UMR 5800, F-33405 Talence Cedex, France;Université de Bordeaux -- LaBRI UMR 5800, F-33405 Talence Cedex, France

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

An acyclic coloring of a graph G is a coloring of its vertices such that: (i) no two adjacent vertices in G receive the same color and (ii) no bicolored cycles exist in G. A list assignment of G is a function L that assigns to each vertex v@?V(G) a list L(v) of available colors. Let G be a graph and L be a list assignment of G. The graph G is acyclically L-list colorable if there exists an acyclic coloring @f of G such that @f(v)@?L(v) for all v@?V(G). If G is acyclically L-list colorable for any list assignment L with |L(v)|=k for all v@?V(G), then G is acyclically k-choosable. In this paper, we prove that every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable.