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Reflection positivity, rank connectivity, and homomorphism of graphs

M. Freedman·L. Lovasz·A. Schrijver
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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.

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M. Freedman, L. Lovasz, A. Schrijver. 2004-04-26. Reflection positivity, rank connectivity, and homomorphism of graphs. https://arxiv.org/abs/math/0404468

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