On Weighted Graph Homomorphisms
نویسندگان
چکیده
For given graphs G and H , let |Hom(G,H)| denote the set of graph homomorphisms from G to H . We show that for any finite, n-regular, bipartite graph G and any finite graph H (perhaps with loops), |Hom(G,H)| is maximum when G is a disjoint union of Kn,n’s. This generalizes a result of J. Kahn on the number of independent sets in a regular bipartite graph. We also give the asymptotics of the logarithm of |Hom(G,H)| in terms of a simply expressed parameter of H . We also consider weighted versions of these results which may be viewed as statements about the partition functions of certain models of physical systems with hard constraints.
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