Computing the partition function for graph homomorphisms

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 GH from pairs of graphs that need to be substantially modified to acquire a color-preserving homomorphism GH.

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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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Mathematics Subject Classification (2000)

  • 15A15
  • 68C25
  • 68W25
  • 60C05