Constraint satisfaction problems for reducts of homogeneous graphs

@inproceedings{Bodirsky2016ConstraintSP,
  title={Constraint satisfaction problems for reducts of homogeneous graphs},
  author={M. Bodirsky and B. Martin and Michael Pinsker and Andr{\'a}s Pongr{\'a}cz},
  booktitle={ICALP},
  year={2016}
}
For $n\geq 3$, let $(H_n, E)$ 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 $H_n$ whose relations are first-order definable in $(H_n,E)$ 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… Expand
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