AMS/MBA 546 (Fall, 2010)
Estie Arkin
Network Flows
Homework Set # 5
Due Thursday, October 14, 2010.
1). Show that the following problems are NPcomplete. You may use reductions from any of the problems
shown NPcomplete 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
2connected
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 2connected. (This may remind you of the minimum spanning
tree problem, in which we look for a subgraph that is 1connected.)
(a). Does the following algorithm work (for all graphs)? Prove or give a counterexample: Sort the edges
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 Fall '08
 Arkin,E
 Graph Theory, Shortest path problem, shortest path, Estie Arkin, shortest path distances

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