(H,C,K) -Coloring: Fast, Easy, and Hard Cases

  • Josep Díaz
  • Maria Serna
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2136)


We define a variant of the H-coloring problem by fixing the number of preimages of a subset C of the vertices of H, thus allowing parameterization. We provide sufficient conditions to guarantee that the problem can be solved in O(kn + f(k, H)) steps where f is a function depending only on the number k of fixed preimages and the graph H, and in O(n k+c) steps where c is a constant independent of k. Finally, we prove that whenever the non parameterized vertices induce in G a graph that is bipartite and loopless the problem is NP-complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Josep Díaz
    • 1
  • Maria Serna
    • 1
  • Dimitrios M. Thilikos
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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