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
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Finding small separators in linear time via treewidth reduction
ACM Transactions on Algorithms (TALG)
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
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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, and we provide a dichotomy theorem determining the H's for which the restrictive H-coloring problem is either NP-complete or polynomial time 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 show that both our results apply also for the list versions and other extensions of the problems.