4. Consider the meta-graph SG of question 3, and suppose that the edges of G have positive integer weights. The weights are not necessarily distinct, so there can be more than one minimum spanning tree (MST) of G. Some vertices of SG will correspond to MSTs of G and the other vertices correspond to spanning trees of G that do not have minimum weight. Prove that the subgraph of SG that is induced by the vertices of SG corresponding to MSTs of G is connected.
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