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The Complexity of the List Homomorphism Problem for Graphs

Authors: László Egri, Andrei Krokhin, Benoit Larose, and Pascal Tesson

Published in: LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)


Abstract
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.

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László Egri, Andrei Krokhin, Benoit Larose, and Pascal Tesson. The Complexity of the List Homomorphism Problem for Graphs. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 335-346, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{egri_et_al:LIPIcs.STACS.2010.2467,
  author =	{Egri, L\'{a}szl\'{o} and Krokhin, Andrei and Larose, Benoit and Tesson, Pascal},
  title =	{{The Complexity of the List Homomorphism Problem for Graphs}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{335--346},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Marion, Jean-Yves and Schwentick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2467},
  URN =		{urn:nbn:de:0030-drops-24675},
  doi =		{10.4230/LIPIcs.STACS.2010.2467},
  annote =	{Keywords: Graph homomorphism, constraint satisfaction problem, complexity, universal algebra, Datalog}
}
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