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Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. Show that if |E|= 3N, the probability that the generated graph contains even a single perfect matching goes to 0 as N→∞

Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. Show that if |E|= 3N, the probability that the generated graph contains even a single perfect matching goes to 0 as N→∞

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
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Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. Show that if |E|= 3N, the probability that the generated graph contains even a single perfect matching goes to 0 as N→∞.

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