Many 3-colorings of triangle-free planar graphs

  • Authors:

  • Carsten Thomassen

  • Affiliations:

  • Department of Mathematics, Technical University of Denmark, DK-2800 Lyngby, Denmark

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2007

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Abstract

Grotzsch proved that every planar triangle-free graph is 3-colorable. We prove that it has at least 2^n^^^1^^^/^^^1^^^2^/^2^0^0^0^0 distinct 3-colorings where n is the number of vertices. If the graph has girth at least 5, then it has at least 2^n^/^1^0^0^0^0 distinct list-colorings provided every vertex has at least three available colors.