Reflection positivity, rank connectivity, and homomorphism of graphs

Details Reflection positivity, rank connectivity, and homomorphism of graphs Reflection positivity, rank connectivity, and homomorphism of graphs

2004-04-26

arxiv.org/abs/math/0404468v1

Mathematics

Combinatorics

17 pages Latex

Scientific paper

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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