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Unformatted text preview: weighted matching relies on something called the weighted node cover which is a generalization of the node cover for the cardinality case. The goal of this prelab exercise is to draw a parallel between the cardinality and the weighted case. A3, B1, C4 and E2 is a maximum (cardinality) matching for the graph below (matching edges are bold). a. Draw an alternating tree to show that the indicated matching is maximum. b. Find a minimum node cover (circle the nodes in the minimum node cover in the original graph). What is the size of the minimum node cover? c. Is there an exposed node (wrt the matching) which is in the minimum node cover? Why? Is there a matching edge with both endpoints in the minimum node cover? Why? A B C D E 1 2 3 4 5...
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 Fall '05
 TROTTER
 Graph Theory, Bipartite graph, minimum node cover

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