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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This note was uploaded on 02/17/2009 for the course MATH 4171 taught by Professor Lax,r during the Spring '08 term at LSU.
 Spring '08
 Lax,R
 Graph Theory

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