Monotone monadic SNP and constraint satisfaction
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
Two algorithms for general list matrix partitions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Full Constraint Satisfaction Problems
SIAM Journal on Computing
Digraph matrix partitions and trigraph homomorphisms
Discrete Applied Mathematics
The Complexity of the List Partition Problem for Graphs
SIAM Journal on Discrete Mathematics
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Finding odd cycle transversals
Operations Research Letters
Dichotomy for tree-structured trigraph list homomorphism problems
Discrete Applied Mathematics
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
Graph partitions with prescribed patterns
European Journal of Combinatorics
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We present a polynomial time algorithm for the 3-Compatible colouring problem, where we are given a complete graph with each edge assigned one of 3 possible colours and we want to assign one of those 3 colours to each vertex in such a way that no edge has the same colour as both of its endpoints. Consequently we complete the proof of a dichotomy for the k-Compatible Colouring problem. The tractability of the 3-Compatible colouring problem has been open for several years and the best known algorithm prior to this paper is due to Feder et al. [SODA'05] --- a quasipolynomial algorithm with a nO(logn/log log n) time complexity. Furthermore our result implies a polynomial algorithm for the Stubborn problem which enables us to finish the classification of all List Matrix Partition variants for matrices of size at most four over subsets of {0, 1} started by Cameron et al. [SODA'04].