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The Complexity of the List Homomorphism Problem for Graphs

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Abstract

We completely classify the computational complexity of the list H-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph H, the problem is either NP-complete, NL-complete, L-complete or is first-order definable; descriptive complexity equivalents are given as well via Datalog and its fragments. Our algebraic characterisations match important conjectures in the study of constraint satisfaction problems.

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Authors and Affiliations

  1. School of Computer Science, McGill University, Montréal, Canada

    László Egri

  2. School of Engineering and Computing Sciences, Durham University, Durham, UK

    Andrei Krokhin

  3. Department of Mathematics and Statistics, Concordia University, Montréal, Canada

    Benoit Larose

  4. Department of Computer Science, Laval University, Quebec City, Canada

    Pascal Tesson

Authors
  1. László Egri
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  2. Andrei Krokhin
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  3. Benoit Larose
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  4. Pascal Tesson
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Corresponding author

Correspondence to Andrei Krokhin.

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Egri, L., Krokhin, A., Larose, B. et al. The Complexity of the List Homomorphism Problem for Graphs. Theory Comput Syst 51, 143–178 (2012). https://doi.org/10.1007/s00224-011-9333-8

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