AMS/MBA 546 (Fall, 2010)Estie ArkinNetwork FlowsHomework Set # 5Due Thursday, October 14, 2010.1). Show that the following problems are NP-complete. You may use reductions from any of the problemsshown 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). GivenG= (N,E), is there a spanning treeTofGsuch that the nodes ofThave degree at most 2?(b). GivenG= (N,E), is there a spanning treeTofGsuch that the nodes ofThave degree at most 3?2). Recall that a graph is2-connectedif there does not exist a node whose removal disconnects the graph(anarticulation node). Given a graph with positive edge weights, consider the problem of trying to find aminimum weight spanning subgraph that is 2-connected. (This may remind you of the minimum spanningtree 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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