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{\bf Geoffrey Grimmett and Svante Janson}
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{\bf Random Even Graphs}
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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--L\"owner evolutions
(SLE).



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