Unformatted text preview: 1 i h 9 8 g 7 d 4 e 5 f 6 c 3 b 2 a Let A = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } , and let B = { a,b,c,d,e,f,g,h,i } . The thick edges are the matching edges. 5. Let G be a bipartite graph with bipartition A,B such that  A  =  B  , and for every nonempty subset D ± A , we have that  N ( D )  >  D  . Prove that, for every edge e ∈ E ( G ), there is a perfect matching containing e . 6. Let K is a matching in a nonbipartite graph G . Show that if K is not maximum, then it admits an augmenting path. (Hint: for any larger matching L , consider only the edges that are in K or L , but not both.)...
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 Spring '09
 M.PEI
 Math, Bipartite graph, perfect matching, Dulmage–Mendelsohn decomposition

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