Unformatted text preview: at all clear to them whether there even exists a spanning tree meeting these conditions, and how to find one if it exists. So this is the problem they put to you: give a polynomial time algorithm that takes G, with each edges labeled X or Y, and either (i) returns a spanning tree with exactly k edges labeled X, or (ii) reports correctly that no such tree exists. 2) Let us say that a graph G = (V, E) is a neartree if it is connected and has at most n + 8 edges, where n = V. Give an algorithm with running time O(n) that takes a neartree G with costs on its edges, and returns the minimum spanning tree of G. You may assume that all edge costs are distinct....
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 Fall '06
 Shamsian
 Networking, Algorithms, Graph Theory, Planar graph, Spanning tree

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