#### Date of Original Version

2-2-2012

#### Type

Article

#### Rights Management

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.

#### DOI

10.1002/rsa.20427

#### Published In

Random Structures and Algorithms, 41, 3, 334-364.