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 de±ned as a spanning tree of G if from among all spanning trees of G the di²erence 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
- Graph Theory, #, Planar graph, Estie Arkin