The complexity of counting homomorphisms seen from the other side

@article{Dalmau2004TheCO,
  title={The complexity of counting homomorphisms seen from the other side},
  author={V. Dalmau and P. Jonsson},
  journal={Theor. Comput. Sci.},
  year={2004},
  volume={329},
  pages={315-323}
}
For every class of relational structures C, let HOM(C, _) be the problem of deciding whether a structure A ∈ C has a homomorphism to a given arbitrary structure B. Grohe has proved that, under a certain complexity-theoretic assumption, HOM(C, _) is solvable in polynomial time if and only if the cores of all structures in C have bounded tree-width. We prove (under a weaker complexity-theoretic assumption) that the corresponding counting problem #HOM(C, _) is solvable in polynomial time if and… Expand
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