Do Problem 22 in Chapter 4 on page 200 of the Kleinberg and Tardos text. Consider a graph on four nodes v1, v2, v3, v4 in which there are edges (v1, v2), (v2, v3), (v3, v4), (v4, v1), of cost 2 each, and an edge (v1, v3) of cost 1.

Question: 22. Consider the Minimum Spanning Tree Problem on an undirected graph G = (V, E), with a cost ce 0 on each edge, where the costs may not all be different. If the costs are not all distinct, there can in general be many distinct minimum-cost solutions. Suppose we are given a spanning tree T CE with the guarantee that for every e e T, e belongs to some minimum-cost spanning tree in G. Can we conclude that T itself must be a minimum-cost spanning tree in G? Give a proof or a counterexample with explanation.