Szegedy (B. Szegedy, Edge coloring models and reflection positivity, Journal of the American Mathematical Society 20, 2007, 969-988.) showed that the partition function of any vertex coloring model is equal to the partition function of a complex edge coloring model. Using some results in geometric invariant theory, we characterize for which vertex coloring model the edge coloring model can be taken to be real valued that is, we characterize which partition functions of vertex coloring models are edge reflection positive. This answers a question posed by Szegedy.
Other (theme 6)
The Scuola Normale Superiore
J. Nešetřil (Jaroslav) , M Pellegrini
Publications of the Scuola Normale Superiore, CRM Series
Spinoza prijs Lex Schrijver
European Conference on Combinatorics, Graph Theory and Applications
Networks and Optimization

Regts, G. (2013). A characterization of edge-reflection positive partition functions of vertex-coloring models. In J Nešetřil & M Pellegrini (Eds.), The Seventh European Conference on Combinatorics, Graph Theory and Applications (pp. 305–311). The Scuola Normale Superiore.