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Unformatted text preview: st cut has size at least k . 4. Let G = ( V, E ) be a 9connected graph and let A, B V with A B = and  A  =  B  = 9. Prove that G has 9 vertexdisjoint paths between A and B . 5. Let us consider the following greedy algorithm for the maximum matching problem. Suppose the input graph is G = ( V, E ) with E = { e 1 , e 2 , ..., e m } . We start with M = . What we do at iteration i (1 i m ) is: if M { e i } is a matching, let M := M { e } ; if M { e i } is not a matching, keep the current M unchanged. After m iterations, we output M . (1) Find a graph G for which the algorithm does not produce a maximum matching. (2) If the algorithm produces a matching of size 2006 from an input graph G , is it possible for G to have a matching of size 4171 or more? Important No Late Homework Will be Accepted...
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 Spring '08
 Lax,R
 Graph Theory

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