COMPUTING THE PARTITION FUNCTION FOR GRAPH HOMOMORPHISMS

Abstract. We introduce the partition function of edge-colored graph homomor-phisms, of which the usual partition function of graph homomorphisms is a special-ization, and present an efficient algorithm to approximate it in a certain domain. Corollaries include efficient algorithms for computing weighted sums approximat-ing 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. 1. Introduction an