Author:
Grimmett Geoffrey,Janson Svante
Abstract
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).
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
9 articles.
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