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  3. 9. let g be a bipartite graph and r ? z>0. prov

9. Let G be a bipartite graph and r ? Z>0. Prove that if G...

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Advance Math

9. Let G be a bipartite graph and r ? Z>0. Prove that if G isr-regular, then G has a perfect matching.1

10. Let G be a simple graph. Prove that the connection relationin G is an equivalence relation on V (G)

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9Proof To prove this we first state a theorem Halls Marriage Theorem Let G be a bipartite graph with bipartition A B Then there is a matching M G which covers A if and only if NX X for every X A Let G be a rregular bipartite graph with bipartition A B Let X A and let t be the number of edges with one end in X Since every vertex in X    See Answer
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