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
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Computers and Intractability: A Guide to the Theory of NP-Completeness
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of 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
On highly ramsey infinite graphs
Journal of Graph Theory
Dichotomy for bounded degree H-colouring
Discrete Applied Mathematics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Combinatorial proof that subprojective constraint satisfaction problems are NP-complete
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
A New Proof of the $H$-Coloring Dichotomy
SIAM Journal on Discrete Mathematics
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We further generalise a construction-the fibre construction-that was developed in an earlier paper of the first two authors. The extension in this paper gives a polynomial-time reduction of CSP(H) for any relational system H to CSP(P) for any relational system P that meets a certain technical partition condition, that of being K"3-partitionable. Moreover, we define an equivalent condition on P, that of being block projective, and using this show that our construction proves NP-completeness for exactly those CSPs that are conjectured to be NP-complete by the CSP dichotomy classification conjecture made by Bulatov, Jeavons and Krohkin, and by Larose and Zadori. We thus provide two new combinatorial versions of the CSP dichotomy classification conjecture. As with our previous version of the fibre construction, we are able to address restricted versions of the dichotomy conjecture. In particular, we reduce the Feder-Hell-Huang conjecture to the CSP dichotomy classification conjecture, and we prove the Kostochka-Nesetril-Smolikova conjecture. Although these results were proved independently by Jonsson et al. and Kun respectively, we give different, shorter, proofs.