Reflection positivity, rank connectivity, and homomorphism of graphs - Freedman, Michael; Lovasz, Laszlo; Schrijver, Alexander (2004)
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.