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Keywords:

  • embedding;
  • edge coloring;
  • Grünbaum coloring;
  • Grünbaum conjecture;
  • triangulation

Abstract

We prove that if G is a triangulation of the torus and χ(G)≠5, then there is a 3-coloring of the edges of G so that the edges bounding every face are assigned three different colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 68–81, 2010