Question: Consider a possible DIVIDE-AND-CONQUER approach to finding a minimal spanning tree in a connected, weighted, graph G. Suppose that we recursively divide the vertices of

Consider a possible DIVIDE-AND-CONQUER approach to finding a minimal spanning tree in a connected, weighted, graph G. Suppose that we recursively divide the vertices of G into two disjoint subsets V1 and V2. We then find a minimal spanning tree T1 for V1 and a minimal spanning tree T2 for V2. Finally we find a minimum weight edge e connecting T1 and T2. We then let T be the graph obtained by combining T1, T2, and e. (a) Is T always a spanning tree? (b) If T is a spanning tree, is it always a minimal spanning tree?

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