A Study of Graph Homomorphisms: Determining the Partition Function

ABSTRACT

We present an efficient algorithm to approximate the partition function of edge-colored graph homomorphisms, which is a specialisation of the more common partition function of graph homomorphisms, and we introduce the partition function of edge-colored graph homomorphisms, which is a specialisation of the usual partition function of graph homomorphisms. 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 between pairs of edge-colored graphs with many color-preserving homomorphisms G H and pairs of graphs that need to be substantially modified to acquire a color-preserving homomorphism G H. This distinction can be made by comparing the numbers of color-preserving homomorphisms

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