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A graph G is a k regular graph if all the vertices of G has...

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Algebra

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A graph G is a k regular graph if all the vertices of G has the same degree k For example Kn is a n 1 regular graph Part A Let G X Y E be a regular bipartite graph prove that X Y Part B Use Hall s theorem to prove that if G X Y E is a regular bipartite graph then there is a matching of size X Part C Let G X Y E be a k regular bipartite graph then the edge set of G can be partitioned into k matchinga which do not share any common edge Hint you may want to use induction

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