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1. Let (G, X, Y) be a bipartite graph. Prove that there exist a matching M of and a subset U of X such that |M| ≥ |N(U)| + |X| − |U|. (Hint: Use König's theorem)

1. Let (G, X, Y) be a bipartite graph. Prove that there exist a matching M of and a subset U of X such that |M| ≥ |N(U)| + |X| − |U|. (Hint: Use König's theorem)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 10EQ
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1. Let (G, X, Y) be a bipartite graph. Prove that there exist a matching M of and a subset U of X such that |M| ≥ |N(U)| + |X| − |U|. (Hint: Use König's theorem)
Transcribed Image Text:1. Let (G, X, Y) be a bipartite graph. Prove that there exist a matching M of and a subset U of X such that |M| ≥ |N(U)| + |X| − |U|. (Hint: Use König's theorem)
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