The color space of a graph

  • Authors:

  • Tommy R. Jensen;Carsten Thomassen

  • Affiliations:

  • Mathematisches Seminar, Universität Hamburg, Bundesstraβe 55, D-20146 Hamburg, Germany;Mathematics Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2000

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Abstract

If k is a prime power, and G is a graph withn vertices, then a k-coloring of G may beconsidered as a vector in GF(k)n.We prove that the subspace of GF(3)nspanned by all 3-colorings of a planar triangle-free graph withn vertices has dimension n. In particular, any suchgraph has at least n - 1 nonequivalent 3-colorings, and theaddition of any edge or any vertex of degree 3 results in a3-colorable graph. © 2000 John Wiley & Sons, Inc. J GraphTheory 34: 234245, 2000