Determine which of the following problems are NP-complete and which are solvable in polynomial time. In each problem you are given an undirected graph G =(V, E), along with:
(a) A set of nodes L ḍ⊆V, and you must find a spanning tree such that its set of leaves includes the set L.
(b) A set of nodes L ⊆ V, and you must find a spanning tree such that its set of leaves is precisely the set L.
(c) A set of nodes L ⊆ V, and you must find a spanning tree such that its set of leaves is included in the set L.
(d) An integer k, and you must find a spanning tree with k or fewer leaves.
(e) An integer k, and you must find a spanning tree with k or more leaves.
(f) An integer k, and you must find a spanning tree with exactly k leaves.
(Hint: All the NP-completeness proofs are by generalization, except for one.)
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