Geodesic
Reflection positivity, rank connectivity, and homomorphism of graphs
Freedman, Michael 1   ; Lovász, László 2   ; Schrijver, Alexander 3
1 Microsoft Institute for Quantum Physics, Santa Barbara, California 93106
2 Microsoft Research, One Microsoft Way, Redmond, Washington 98052
3 CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
Journal of the American Mathematical Society, Tome 20 (2007) no. 1, pp. 37-51 Cet article a éte moissonné depuis la source American Mathematical Society

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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 coloring models.
DOI : 10.1090/S0894-0347-06-00529-7

Freedman, Michael  1   ; Lovász, László  2   ; Schrijver, Alexander  3

1 Microsoft Institute for Quantum Physics, Santa Barbara, California 93106
2 Microsoft Research, One Microsoft Way, Redmond, Washington 98052
3 CWI, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands 
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Freedman, Michael; Lovász, László; Schrijver, Alexander. Reflection positivity, rank connectivity, and homomorphism of graphs. Journal of the American Mathematical Society, Tome 20 (2007) no. 1, pp. 37-51. doi: 10.1090/S0894-0347-06-00529-7

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