Theory of Computing Systems

, Volume 51, Issue 2, pp 143–178

The Complexity of the List Homomorphism Problem for Graphs

  • László Egri
  • Andrei Krokhin
  • Benoit Larose
  • Pascal Tesson


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.


Constraint satisfaction problem List homomorphism Complexity Universal algebra Datalog 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • László Egri
    • 1
  • Andrei Krokhin
    • 2
  • Benoit Larose
    • 3
  • Pascal Tesson
    • 4
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.School of Engineering and Computing SciencesDurham UniversityDurhamUK
  3. 3.Department of Mathematics and StatisticsConcordia UniversityMontréalCanada
  4. 4.Department of Computer ScienceLaval UniversityQuebec CityCanada

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