In this exercise we prove a theorem of 0ystein ?re.
Chapter , Problem 32E(choose chapter or problem)
Problem 32E
In this exercise we prove a theorem of 0ystein ∅re. Suppose that G = (V. E) is a bipartite graph with bipartition (V1, V2) and that A ⊆ V1. Show that the maximum number of vertices of V1 that are the endpoints of a matching of G equals |V1| – maxA⊆v1, def(A). where def(A) = |A| − |N(A)|. (Here, def (A) is called the deficiency of A.) [Hint: Form a larger graph by adding maxA⊆v1,def(A) new vertices to V2 and connect all of them to the vertices of V1.]
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