forest


Negative association in uniform forests ★★

Author(s): Pemantle

\begin{conjecture} Let $G$ be a finite graph, let $e,f \in E(G)$, and let $F$ be the edge set of a forest chosen uniformly at random from all forests of $G$. Then \[ {\mathbb P}(e \in F \mid f \in F}) \le {\mathbb P}(e \in F) \] \end{conjecture}

Keywords: forest; negative association

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