English

Reflection positivity, rank connectivity, and homomorphism of graphs

Combinatorics 2007-05-23 v1 Mathematical Physics math.MP

Abstract

It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rank-connectivity. In terms of statistical physics, this can be viewed as a characterization of partition functions of vertex models.

Keywords

Cite

@article{arxiv.math/0404468,
  title  = {Reflection positivity, rank connectivity, and homomorphism of graphs},
  author = {M. Freedman and L. Lovasz and A. Schrijver},
  journal= {arXiv preprint arXiv:math/0404468},
  year   = {2007}
}

Comments

17 pages Latex