Edge-reflection positivity and weighted graph homomorphisms
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| Publication date | 01-2015 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | Issue number | 129 |
| Pages (from-to) | 80-92 |
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| Abstract |
B. Szegedy (2007) [12] showed that the number of homomorphisms into a weighted graph is equal to the partition function of a complex edge-coloring model. Using some results in geometric invariant theory, we characterize for which weighted graphs the edge-coloring model can be taken to be real-valued that is, we characterize for which weighted graphs the number of homomorphisms into them is edge-reflection positive. In particular, we determine explicitly for which simple graphs the number of homomorphisms into them is equal to the partition function of a real edge-coloring model. This answers a question posed by Szegedy.
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| Document type | Article |
| Language | English |
| Published at |
https://doi.org/10.1016/j.jcta.2014.09.006
(Final published version)
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