On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Colorings and homomorphisms of degenerate and bounded degree graphs
Discrete Mathematics
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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
The Complexity of the Extendibility Problem for Finite Posets
SIAM Journal on Discrete Mathematics
On sparse graphs with given colorings and homomorphisms
Journal of Combinatorial Theory Series B
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
H-Coloring dichotomy revisited
Theoretical Computer Science - Graph colorings
A Probabilistic Approach to the Dichotomy Problem
SIAM Journal on Computing
A combinatorial constraint satisfaction problem dichotomy classification conjecture
European Journal of Combinatorics
A New Proof of the $H$-Coloring Dichotomy
SIAM Journal on Discrete Mathematics
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We introduce a new general polynomial-time constructionthe fibre construction- which reduces any constraint satisfaction problem CSP(H) to the constraint satisfaction problem CSP(P), where P is any subprojective relational structure. As a consequence we get a new proof (not using universal algebra) that CSP(P) is NP-complete for any subprojective (and thus also projective) relational structure. This provides a starting point for a new combinatorial approach to the NP-completeness part of the conjectured Dichotomy Classification of CSPs, which was previously obtained by algebraic methods. This approach is flexible enough to yield NP-completeness of coloring problems with large girth and bounded degree restrictions.