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H-Colorings of Large Degree Graphs

  • Josep Díaz
  • Jaroslav Nešetřil
  • Maria Serna
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2510)

Abstract

We consider the H-coloring problem on graphs with vertices of large degree. We prove that for H an odd cycle, the problem belongs to P. We also study the phase transition of the problem, for an infinite family of graphs of a given chromatic number, i.e. the threshold density value for which the problem changes from P to NP-complete. We extend the result for the case that the input graph has a logarithmic size of small degree vertices. As a corollary, we get a new result on the chromatic number; a new family of graphs, for which computing the chromatic number can be done in polynomial time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Josep Díaz
    • 1
  • Jaroslav Nešetřil
    • 2
  • Maria Serna
    • 1
  • Dimitrios M. Thilikos
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica deBarcelonaSpain
  2. 2.DIMATIA-ITI and Department of Applied MathematicsCharles UniversityPragueCzech Republic

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