Problem 5 (6 points). Let G be a connected weighted undirected graph with n nodes and m edges. The weight of edge e is represented as we. We define a minimum-maximum spanning tree to be a spanning tree T that minimizes the quantity Y=maxeTwe A minimum-maximum spanning tree has the smallest maximum edge weight of all possible spanning tree. (a) (3 points) Prove that a minimum spanning tree of graph G is always a minimummaximum spanning tree for G. (b) (3 points) Show that a minimum-maximum spanning tree is not necessary a minimum spanning tree by giving a counter-example