Star list chromatic number of planar subcubic graphs

  • Authors:

  • Min Chen;André Raspaud;Weifan Wang

  • Affiliations:

  • Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004 and LaBRI UMR CNRS 5800, Université Bordeaux I, Talence Cedex, France 33405;LaBRI UMR CNRS 5800, Université Bordeaux I, Talence Cedex, France 33405;Department of Mathematics, Zhejiang Normal University, Jinhua, China 321004

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

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Abstract

A proper coloring of the vertices of a graph G is called a star-coloring if the union of every two color classes induces a star forest. The graph G is L-star-colorable if for a given list assignment L there is a star-coloring 驴 such that 驴(v)驴L(v). If G is L-star-colorable for any list assignment L with |L(v)|驴k for all v驴V(G), then G is called k-star-choosable. The star list chromatic number of G, denoted by $\chi_{s}^{l}(G)$ , is the smallest integer k such that G is k-star-choosable. In this paper, we prove that every planar subcubic graph is 6-star-choosable.