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Computing the partition function for graph homomorphisms
We introduce the partition function of edge-colored graph homomorphisms, of
which the usual partition function of graph homomorphisms is a specialization,
and present an efficient algorithm to approximate it in a certain domain.
Corollaries include efficient algorithms for computing weighted sums
approximating the number of k-colorings and the number of independent sets in a
graph, as well as an efficient procedure to distinguish pairs of edge-colored
graphs with many color-preserving homomorphisms G --> H from pairs of graphs
that need to be substantially modified to acquire a color-preserving
homomorphism G --> H.Comment: constants are improved, following a suggestion by B. Buk
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