4204hw2 - S in the graph G to be a vertex cover if all...

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Combinatorics II (MAD 4204) — Spring 2011 Due Wednesday 1/26/2011 Homework #2 1 Let G be a bipartite graph, and suppose that vw is an edge of G . Prove either v or w has the property that every maximum matching of G contains an edge incident to this vertex. Note: Of course, every maximum matching of G contains an edge incident to either v or w . This question is asking for something stronger, however. In Homework #1, we deFned a set of vertices
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Unformatted text preview: S in the graph G to be a vertex cover if all edges of G have at least one of their vertices in S . Let ( G ) denote the size of the smallest vertex cover of G and let ( G ) denote the size of its maximum matching. We proved the following theorem: K onigs Theorem. In any bipartite graph G , ( G ) = ( G ). 2 Prove Halls Marriage Theorem from K onigs Theorem....
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