On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Core-like properties of infinite graphs and structures
Selected papers of the 14th British conference on Combinatorial conference
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Cores and compactness of infinite directed graphs
Journal of Combinatorial Theory Series B
The complexity of G-free colourability
Proceedings of an international symposium on Graphs and combinatorics
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A shorter model theory
Closure properties of constraints
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra
Journal of the ACM (JACM)
On determining the consistency of partial descriptions of trees
ACL '94 Proceedings of the 32nd annual meeting on Association for Computational Linguistics
A rendezvous of logic, complexity, and algebra
ACM SIGACT News
A rendezvous of logic, complexity, and algebra
ACM Computing Surveys (CSUR)
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Collapsibility in infinite-domain quantified constraint satisfaction
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Qualitative temporal and spatial reasoning revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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A relational structure is a core, if all endomorphisms are embeddings. This notion is important for the classification of the computational complexity of constraint satisfaction problems. It is a fundamental fact that every finite structure S has a core, i.e., S has an endomorphism e such that the structure induced by e(S) is a core; moreover, the core is unique up to isomorphism. We prove that this result remains valid for ω-categorical structures, and prove that every ω-categorical structure has a core, which is unique up to isomorphism, and which is again ω-categorical. We thus reduced the classification of the complexity of constraint satisfaction problems with ω-categorical templates to the classifiaction of constraint satisfaction problems where the templates are ω-categorical cores. If Γ contains all primitive positive definable relations, then the core of Γ admits quantifier elimination. We discuss further consequences for constraint satisfaction with ω-categorical templates.