Let G = (V, E) be bipartite graph, with vertex partition V = XuY. Assume further that • every z in X has the same degree dx 2 1, and • every y in Y has the same degree dy 21. (a) Prove that = %3D (b) Assuming without loss of generality that dx > dy, show that there exists at least one matching M C E with number of edges |M| = |X|.
Let G = (V, E) be bipartite graph, with vertex partition V = XuY. Assume further that • every z in X has the same degree dx 2 1, and • every y in Y has the same degree dy 21. (a) Prove that = %3D (b) Assuming without loss of generality that dx > dy, show that there exists at least one matching M C E with number of edges |M| = |X|.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 74EQ
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