On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Finding good approximate vertex and edge partitions is NP-hard
Information Processing Letters
List homomorphisms to reflexive graphs
Journal of Combinatorial Theory Series B
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
(H, C, K)-Coloring: Fast, Easy, and Hard Cases
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Dichotomies for classes of homomorphism problems involving unary functions
Theoretical Computer Science
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We define a variant of the H-coloring problem where the number of preimages of certain vertices is predetermined as part of the problem input. We consider the decision and the counting version of the problem; namely the restrictive H-coloring and the restrictive # H- coloring problems. We provide a dichotomy theorem characterizing the H's for which the restrictive H-coloring problem is either NP-complete or polynomially solvable. Moreover, we prove that the same criterion discriminates the #P-complete and the polynomially solvable cases of the restrictive #H-coloring problem. Finally, we prove that both results apply also to the list versions of the above problems.