Constraint satisfaction problems for reducts of homogeneous graphs

Bodirsky, Manuel, Martin, Barnaby, Pinsker, Michael and Pongrácz, András (2016) Constraint satisfaction problems for reducts of homogeneous graphs. In: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), 12-15 Jul 2016, Rome, Italy. (doi:10.4230/LIPIcs.ICALP.2016.119)

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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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Article number = 119
Research Areas: A. > School of Science and Technology > Computer Science
Item ID: 24162
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Depositing User: Bade Ajibade
Date Deposited: 23 Apr 2018 15:11
Last Modified: 07 Apr 2019 11:39
ISBN: 9783959770132

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