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The Complexity of the List Homomorphism Problem for Graphs Egri, László Krokhin, Andrei Larose, Benoit Tesson, Pascal Graph homomorphism constraint satisfaction problem complexity universal algebra Datalog We completely classify the computational complexity of the list $\bH$-colouring problem for graphs (with possible loops) in combinatorial and algebraic terms: for every graph $\bH$ 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik László Egri and Andrei Krokhin and Benoit Larose and Pascal Tesson 2010 Is Part Of LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2010.2467 urn:nbn:de:0030-drops-24675 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2467 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode