1. Let G be a k-regular bipartite graph. Use Corollary 3.1.13 to prove that G can...

1. Let G be a k-regular bipartite graph. Use Corollary 3.1.13 to prove that G can be decomposed into r-factors iff r divides k.

Expert Solution

Colby Messinger answered 2 years ago

1) a) Let k ≥ 2 and let G be a k-regular bipartite graph. Prove that G...

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Let G be a bipartite graph with 107 left vertices and 20 right vertices. Two vertices...

Let G be a bipartite graph with 107 left vertices and 20 right vertices. Two vertices u, v are called twins if the set of neighbors of u equals the set of neighbors of v (triplets, quadruplets etc are defined similarly). Show that G has twins. Bonus: Show that G has triplets. What about quadruplets, etc.?

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