# Spanning tree of a strongly connected directed graph.

Given a strongly connected directed graph $G=(V,E)$, and a node $r \in V$. Let $T_r$ be the set of spanning trees of $G$ with $r$ as root and all edges pointing to $r$. Is is it possible that there is an edge $e$ such that for all $t \in T_r$, we have $e \in E(Tr)$? In other words, is it possible that there is a directed edge of $G$ belongs to all possible spanning trees with $r$ as root?

BTW : My guess is that it is impossible.

Edit : I meant to say "directed graph"

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