Question: 5. (3 points) Suppose you are given an undirected graph G = (V, E) and two nodes s and t such that all paths between

5. (3 points) Suppose you are given an undirected graph G

5. (3 points) Suppose you are given an undirected graph G = (V, E) and two nodes s and t such that all paths between s and t have length strictly greater than VI/2. Show that there will exist a nodev #st such that removing v will disconnects and t. That is, consider the graph G' obtained by removing v and its edges from G. Then there is no path between s and t in G'. Design an algorithm to find such a node. Give pseudocode and discuss correctness and running time. (Hint: Use BFS.)

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