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 n2 / d-1. Assume G is connected.