# Pemantle, Robin

## 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