10. Let s and t be two specific vertices of an undirected connected simple graph G (V, E) on n = |v| vertices, where any path between s and t in G consists of at least n/2+ 1 vertices. Show that there is a vertex vEV, vt s and v t, such that any path from s to t passes through v. Also, provide an algorithm, running in O(VI+E) time, for identifying such a vertex v for a given pair of vertices s,tEV. (Note that by removing e from G, we disconnect s and t.) A student pointed out that for this question to make sense it should be at least n/22 vertices in the path. Otherwise there is a simple example with 4 vertices (a cycle where the statement is not true. Please modify the Ist statement where you replace n/2 + 1 by n/2 +2. Thanks for noticing this