10.1184/R1/6478367.v1 Alan Frieze Alan Frieze Pall Melsted Pall Melsted Maximum Matchings in Random Bipartite Graphs and the Space Utilization of Cuckoo Hash Tables Carnegie Mellon University 2012 random bipartite graph Cuckoo Hashing 2012-02-02 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/Maximum_Matchings_in_Random_Bipartite_Graphs_and_the_Space_Utilization_of_Cuckoo_Hash_Tables/6478367 <p>We study the the following question in Random Graphs. We are given two disjoint sets <em>L</em>,<em>R</em> with |<em>L</em>| = <em>n</em> and |<em>R</em>| = <em>m</em>. We construct a random graph <em>G</em> by allowing each <em>x</em>∈<em>L</em> to choose <em>d</em> random neighbours in <em>R</em>. The question discussed is as to the size μ(<em>G</em>) of the largest matching in <em>G</em>. When considered in the context of Cuckoo Hashing, one key question is as to when is μ(<em>G</em>) = <em>n</em> whp? We answer this question exactly when <em>d</em> is at least three.</p>