Note: A note on entire choosability of plane graphs

  • Authors:

  • Wei Dong

  • Affiliations:

  • -

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2012

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Abstract

A plane graph is called entirely k-choosable if for any list assignment L such that |L(x)|=k for each x@?V(G)@?E(G)@?F(G), we can assign each element x a color from its list such that any two elements that are adjacent or incident receive distinct colors. Wang and Lih (2008) [5] conjectured that every plane graph is entirely (@D+4)-choosable and showed that the conjecture is true if @D=12. In this note, we prove that (1) Every plane graph G with @D=7 is entirely (@D+4)-choosable. (2) Every plane graph G with @D=6 is entirely (@D+5)-choosable.