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Prove: an edge e of a connected undirected simple graph G is a cut-edge if and only if it belongs to every spanning tree of G.

Pretty lost on this one. What's a way to connect cut-edges to tree, and how would one go about proving this?

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  • $\begingroup$ Hint: Prove that a cut edge can never be part of a cycle. $\endgroup$ – platty Aug 14 '17 at 14:17
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Here are two facts you could use to prove this.

An edge $e\in E(G)$ is a cut-edge $\Longleftrightarrow$ $G-e$ is disconnected.

This is the definition.

A graph $G$ is disconnected $\Longleftrightarrow$ $G$ has no spanning trees.

This connects spanning trees with connection.

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