Constraint Satisfaction Problems for Reducts of Homogeneous Graphs

Bodirsky, Manuel; Martin, Barnaby; Pinsker, Michael; Pongrácz, András

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.

Citation

Bodirsky, M., Martin, B., Pinsker, M., & Pongrácz, A. (2016). Constraint Satisfaction Problems for Reducts of Homogeneous Graphs. In I. Chatzigiannakis, M. Mitzenmacher, Y. Rabani, & D. Sangiorgi (Eds.), 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, Rome, Italy, July 12–15, 2016. https://doi.org/10.4230/lipics.icalp.2016.119

• Presentation Conference Type: Conference Paper (Published)
• Conference Name: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy
• Start Date: Jul 12, 2016
• End Date: Jul 15, 2016
• Acceptance Date: Apr 15, 2016
• Publication Date: Aug 1, 2016
• Deposit Date: Oct 14, 2016
• Publicly Available Date: Oct 17, 2016
• Series Title: LIPIcs : Leibniz international proceedings in informatics
• Series Number: 55
• Series ISSN: 1868-8969
• Book Title: 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, Rome, Italy, July 12–15, 2016.
• DOI: https://doi.org/10.4230/lipics.icalp.2016.119
• Public URL: https://durham-repository.worktribe.com/output/1150163
• Related Public URLs: https://arxiv.org/abs/1602.05819