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Combinatorica

, Volume 37, Issue 4, pp 633–650 | Cite as

Computing the partition function for graph homomorphisms

  • Alexander BarvinokEmail author
  • Pablo Soberón
Original paper

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.

Mathematics Subject Classification (2000)

15A15 68C25 68W25 60C05 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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