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Consider the following problem: give a graph G and a subset S of its vertices, find a spanning tree of G such that the set of leaves of that spanning tree contain the set S. Prove or disprove that this problem is NP-complete.

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Let T be the spanning tree containing all vertices of S.
Then G\S (i.e. remove vertices of S from G) is a connected graph.

Then, for every node from S there should be an edge (of the spanning tree) such that it connects it to a vertex that is not in S....

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