eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-08-23
119:1
119:14
10.4230/LIPIcs.ICALP.2016.119
article
Constraint Satisfaction Problems for Reducts of Homogeneous Graphs
Bodirsky, Manuel
Martin, Barnaby
Pinsker, Michael
Pongrácz, András
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol055-icalp2016/LIPIcs.ICALP.2016.119/LIPIcs.ICALP.2016.119.pdf
Constraint Satisfaction
Homogeneous Graphs
Computational Complexity
Universal Algebra
Ramsey Theory