Towards a Trichotomy for Quantified H-Coloring

  • Barnaby Martin
  • Florent Madelaine
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)


Hell and Nešetřil proved that the H-colouring problem is NP-complete if, and only if, H is bipartite. In this paper, we investigate the complexity of the quantified H-colouring problem (a restriction of the quantified constraint satisfaction problem to undirected graphs). We introduce this problem using a new two player colouring game. We prove that the quantified H-colouring problem is:

1. tractable, if H is bipartite;

2. NP-complete, if H is not bipartite and not connected; and,

3. Pspace-complete, if H is connected and has a unique cycle, which is of odd length.

We conjecture that the last case extends to all non-bipartite connected graphs.


Bipartite Graph Constraint Satisfaction Problem Winning Strategy Universal Variable Unique Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Barnaby Martin
    • 1
  • Florent Madelaine
    • 1
  1. 1.Department of Computer ScienceUniversity of DurhamU.K.

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