Let G be a weighted, connected, undirected graph, and let V1 and V2 be a partition of the vertices of G into two disjoint nonempty sets. Furthermore, let e be an edge in the minimum spanning tree for G such that e has one endpoint in V1 and the other in V2. Give an example that shows that e is not necessarily the smallest- weight edge that has one endpoint in V1 and the other in V2.

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