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hw5 - AMS/MBA 546(Fall 2010 Estie Arkin Network Flows...

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AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows Homework Set # 5 Due Thursday, October 14, 2010. 1). Show that the following problems are NP-complete. You may use reductions from any of the problems shown NP-complete by Karp (3SAT, 3 dimensional matching, partition, vertex cover, Hamilton cycle/path, or clique), or any other problem discussed in class. Remember to also show the problem is in NP. (a). Given G = ( N,E ), is there a spanning tree T of G such that the nodes of T have degree at most 2? (b). Given G = ( N,E ), is there a spanning tree T of G such that the nodes of T have degree at most 3? 2). Recall that a graph is 2-connected if there does not exist a node whose removal disconnects the graph (an articulation node ). Given a graph with positive edge weights, consider the problem of trying to find a minimum weight spanning subgraph that is 2-connected. (This may remind you of the minimum spanning tree problem, in which we look for a subgraph that is 1-connected.) (a). Does the following algorithm work (for all graphs)? Prove or give a counterexample: Sort the edges
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