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Computing the partition function for graph homomorphisms

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Abstract

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 effcient algorithms for computing weighted sums approximating the number of k-colorings and the number of independent sets in a graph, as well as an effcient 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1043, USA

    Alexander Barvinok & Pablo Soberón

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  1. Alexander Barvinok
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  2. Pablo Soberón
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Correspondence to Alexander Barvinok.

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Barvinok, A., Soberón, P. Computing the partition function for graph homomorphisms. Combinatorica 37, 633–650 (2017). https://doi.org/10.1007/s00493-016-3357-2

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  • DOI: https://doi.org/10.1007/s00493-016-3357-2

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