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Harmonious Coloring on Subclasses of Colinear Graphs

  • Kyriaki Ioannidou
  • Stavros D. Nikolopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5942)

Abstract

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 NP-completeness results of the harmonious coloring problem on subclasses of chordal and co-chordal graphs, we prove that the problem remains NP-complete for split undirected path graphs; we also prove that the problem is NP-complete for colinear graphs by showing that split undirected path graphs form a subclass of colinear graphs. Moreover, we provide a polynomial solution for the harmonious coloring problem for the class of split strongly chordal graphs, the interest of which lies on the fact that the problem has been proved to be NP-complete on both split and strongly chordal graphs.

Keywords

Harmonious coloring colinear coloring colinear graphs split graphs undirected path graphs strongly chordal graphs complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kyriaki Ioannidou
    • 1
  • Stavros D. Nikolopoulos
    • 1
  1. 1.Department of Computer ScienceUniversity of IoanninaIoanninaGreece

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