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