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Enumerating Homomorphisms Bulatov, Andrei A. Dalmau, Victor Grohe, Martin Marx, Daniel The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Andrei A. Bulatov and Victor Dalmau and Martin Grohe and Daniel Marx 2009 Is Part Of LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2009.1838 urn:nbn:de:0030-drops-18385 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1838 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode