# The complexity of counting graph homomorphisms

@article{Dyer2000TheCO,
title={The complexity of counting graph homomorphisms},
author={M. Dyer and Catherine S. Greenhill},
journal={Random Struct. Algorithms},
year={2000},
volume={17},
pages={260-289}
}
• Published 2000
• Computer Science
• Random Struct. Algorithms
The problem of counting homomorphisms from a general graph G to a fixed graph H is a natural generalisation of graph colouring, with important applications in statistical physics. The problem of deciding whether any homomorphism exists was considered by Hell and Nešetřil. They showed that decision is NPcomplete unless H has a loop or is bipartite; otherwise it is in P. We consider the problem of exactly counting such homomorphisms, and give a similarly complete characterisation. We show that… Expand
178 Citations
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