Date of Original Version
This is the accepted version of the article which has been published in final form at http://dx.doi.org/10.1002/rsa.20427
Abstract or Description
We study the the following question in Random Graphs. We are given two disjoint sets L,R with |L| = n and |R| = m. We construct a random graph G by allowing each x∈L to choose d random neighbours in R. The question discussed is as to the size μ(G) of the largest matching in G. When considered in the context of Cuckoo Hashing, one key question is as to when is μ(G) = n whp? We answer this question exactly when d is at least three.
Random Structures and Algorithms, 41, 3, 334-364.