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Unformatted text preview: k red edges, and there is a spanning tree T with k red edges. Show that for all k , k k k there is a spanning tree with exactly k red edges. 3). (AMO 13.34) We are given an undirected, connected graph G = ( V,E ) with (nonnegative) weightss on the edges w ij . A balanced spanning tree is dened as a spanning tree of G if from among all spanning trees of G the dierence between the maximum edge weight and the minimum edge weight is as small as possible. Describe a polynomial time algorithm for nding a balanced spanning tree. Make sure to state the running time of your algorithm....
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 Fall '08
 Arkin,E

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