Note: The harmonious coloring problem is NP-complete for interval and permutation graphs

  • Authors:

  • Katerina Asdre;Kyriaki Ioannidou;Stavros D. Nikolopoulos

  • Affiliations:

  • Department of Computer Science, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece;Department of Computer Science, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece;Department of Computer Science, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

In this paper, we prove that the harmonious coloring problem is NP-complete for connected interval and permutation graphs. Given a simple graph G, a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number is the least integer k for which G admits a harmonious coloring with k colors. Extending previous work on the NP-completeness of the harmonious coloring problem when restricted to the class of disconnected graphs which are simultaneously cographs and interval graphs, we prove that the problem is also NP-complete for connected interval and permutation graphs.