Random even graphs

Geoffrey Grimmett; Svante Janson

Random even graphs

Probability 2009-03-25 v3 Mathematical Physics math.MP

Authors: Geoffrey Grimmett , Svante Janson

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 $\frac 12 \pc$ , where $\pc$ 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--L\"owner evolutions (SLE).

Keywords

random graphs preferential attachment graph theory

Cite

@article{arxiv.0709.3039,
  title  = {Random even graphs},
  author = {Geoffrey Grimmett and Svante Janson},
  journal= {arXiv preprint arXiv:0709.3039},
  year   = {2009}
}

Comments

Version 2 includes material about random even graphs with general values of the edge-parameter p, together with a coupling-from-the-past algorithm for their simulation. Version 3 includes a treatment of infinite graphs, and is to appear in the Electronic Journal of Combinatorics

Random even graphs

Abstract

Keywords

Cite

Comments

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