Question: Prove Lemma 12.3. Let G = (V, E) be a loop-free connected undirected graph with z V. The vertex z is an articulation point

Prove Lemma 12.3.
Let G = (V, E) be a loop-free connected undirected graph with z ∈ V. The vertex z is an articulation point of G if and only if there exist distinct x, y ∈ V with x ≠ z, y ≠ z, and such that every path in G connecting x and y contains the vertex z.

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