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DOI: 10.4230/LIPIcs.ICALP.2016.119
Constraint Satisfaction Problems for Reducts of Homogeneous Graphs

Authors: Manuel Bodirsky, Barnaby Martin, Michael Pinsker, and András Pongrácz

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
For n >= 3, let (Hn, E) denote the n-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on n vertices. We show that for all structures Gamma with domain Hn whose relations are first-order definable in (Hn, E) the constraint satisfaction problem for Gamma is either in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete.
Cite as

Manuel Bodirsky, Barnaby Martin, Michael Pinsker, and András Pongrácz. Constraint Satisfaction Problems for Reducts of Homogeneous Graphs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 119:1-119:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2016.119,
  author =	{Bodirsky, Manuel and Martin, Barnaby and Pinsker, Michael and Pongr\'{a}cz, Andr\'{a}s},
  title =	{{Constraint Satisfaction Problems for Reducts of Homogeneous Graphs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{119:1--119:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.119},
  URN =		{urn:nbn:de:0030-drops-62543},
  doi =		{10.4230/LIPIcs.ICALP.2016.119},
  annote =	{Keywords: Constraint Satisfaction, Homogeneous Graphs, Computational Complexity, Universal Algebra, Ramsey Theory}
}
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