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Question 2: A bipartite graph with 2n vertices (namely |V1| = |V2| = n) is d-regular...

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Question 2: A bipartite graph with 2n vertices (namely |V1| =|V2| = n) is d-regular if and only if the degree of every vertex inV1 ∪ V2 is exactly d. Show that a d-regular bipartite graph alwayshas a perfect matching (a matching of size n that includes allvertices).

***Remarks: All the graphs here are without self loops andparallel or anti-parallel edges. A network is a directed graph withsource s and sink t and capacity ce > 0 on every edge e. In allthe algorithms, always explain their correctness and analyze theircomplexity. The complexity should be as small as possible. Acorrect algorithm with large complexity, may not get full credit.The number of vertices is denoted by n, and the number of edges bym. ***

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3.7 Ratings (332 Votes)
Let G be a bipartite graph with 2n vertices v1v2n is d regular That means degree of each vertex of G either its from v1 or from v2 is d Thus degree of each vertex from v1 U v2 is d exactly Conversely let degree of each vertex from v1 U v2 is    See Answer
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