A new line of attack on the dichotomy conjecture
Proceedings of the forty-first annual ACM symposium on Theory of computing
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
A combinatorial constraint satisfaction problem dichotomy classification conjecture
European Journal of Combinatorics
Decidable relationships between consistency notions for constraint satisfaction problems
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Congruence Distributivity Implies Bounded Width
SIAM Journal on Computing
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Low-level dichotomy for quantified constraint satisfaction problems
Information Processing Letters
An algebraic theory of complexity for valued constraints: establishing a Galois connection
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Submodularity on a tree: unifying L-convex and bisubmodular functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
QCSP on partially reflexive forests
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The dichotomy of list homomorphisms for digraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Containment, equivalence and coreness from CSP to QCSP and beyond
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Weak near-unanimity functions and digraph homomorphism problems
Theoretical Computer Science
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Graph partitions with prescribed patterns
European Journal of Combinatorics
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Bang-Jensen and Hell conjectured in 1990 (using the language of graph homomorphisms) a constraint satisfaction problem (CSP) dichotomy for digraphs with no sources or sinks. The conjecture states that the CSP for such a digraph is tractable if each component of its core is a cycle and is $NP$-complete otherwise. In this paper we prove this conjecture and, as a consequence, a conjecture of Bang-Jensen, Hell, and MacGillivray from 1995 classifying hereditarily hard digraphs. Further, we show that the CSP dichotomy for digraphs with no sources or sinks agrees with the algebraic characterization conjectured by Bulatov, Jeavons, and Krokhin in 2005.