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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 ⊆E with the guarantee that for every 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 explana
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