Let G = (V,E) be a simple graph which is weighted, undirected, and connected. Sup- pose G contains a unique edge having the largest weight. Let emax be this edge. Suppose removing emax in G does not disconnect G. Prove that any minimum spanning tree of G must not contain the edge emax. Hint: Prove by contradiction. (Consider on the contrary that the MST contains emax. Think in this way: Can we replace this edge by some other edge to reduce the total weight?)

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