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PROBLEM 3 (25 POINTS) Let G(V, E) be an undirected and unweighted graph with n nodes. Let T1, T2, ...,Tk be k=n - 1 distinct
PROBLEM 3 (25 POINTS) Let G(V, E) be an undirected and unweighted graph with n nodes. Let T1, T2, ...,Tk be k=n - 1 distinct spanning trees of G. Devise a polynomial-time algorithm that finds a spanning tree T = (V,ET) in G that contains at least one edge from each Ti. (Prove correctness and polynomial runtime.) Definition: two trees (or for that matter any graphs) on a set of nodes are distinct, if they differ in at least one edge. PROBLEM 3 (25 POINTS) Let G(V, E) be an undirected and unweighted graph with n nodes. Let T1, T2, ...,Tk be k=n - 1 distinct spanning trees of G. Devise a polynomial-time algorithm that finds a spanning tree T = (V,ET) in G that contains at least one edge from each Ti. (Prove correctness and polynomial runtime.) Definition: two trees (or for that matter any graphs) on a set of nodes are distinct, if they differ in at least one edge
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