2. Let G = (V, E) a directed imit-capaacitj,r graph, i.e., C(e) = 1 for each s E E. o (Menger's Theorem) Given an integer k > [1, show that G has I: edge disjoint paths from s to t if and only if there is an s-t ow of value I: in G. (This shows that the maximum mmlber of edge disjoint paths from 3 to t is exactly the value of the maximum s-t ow.) a Let G = (V, E) be a directed graph and let u, v, m be distinct vertices. Suppose there are k edge disjoint paths from u to 'u in G, and k edge disjoint paths from 1: to w in G. Note that the paths from "u, to 1) can share edges with the paths from v to w. Prove that there are R: edge disjoint paths from a to 'w in G. [Hint: Use Maxow-Mjncut or the Menger's theorem.]