Geodesic
Random even graphs
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We study a random even subgraph of a finite graph $G$ with a general edge-weight $p\in(0,1)$. We demonstrate how it may be obtained from a certain random-cluster measure on $G$, and we propose a sampling algorithm based on coupling from the past. A random even subgraph of a planar lattice undergoes a phase transition at the parameter-value ${1\over2} p_{\rm c}$, where $p_{\rm c}$ is the critical point of the $q=2$ random-cluster model on the dual lattice. The properties of such a graph are discussed, and are related to Schramm–Löwner evolutions (SLE).
DOI : 10.37236/135
Classification : 05C80, 60K35
Mots-clés : random graph, even subgraph, Ising model, random cluster model 
@article{10_37236_135,
     author = {Geoffrey Grimmett and Svante Janson},
     title = {Random even graphs},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/135},
     zbl = {1214.05155},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/135/}
}
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Geoffrey Grimmett; Svante Janson. Random even graphs. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/135

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