Let G = (V,E) be an undirected, unweighted graph with n = |V| vertices.

The distance between two vertices u,v ∈ G is the length of the shortest path between them. A vertex cut of G is a subset S ⊆ V such that removing the vertices in S (as well as incident edges) disconnects G.
Show that if there exist u, v ∈ G of distance d > 1 from each other, that there exists a vertex cut of size at most n−2 / d-1. Assume G is connected.

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