Random bipartite graphs G(k,n,p) have the normalized matching property with a sharp threshold at p = log n / k, and Thomason pseudorandom bipartite graphs admit the property after deletion of a vanishingly small vertex set.
Anderson, Some problems in combinatorial number theory, PhD thesis, University of Not- tingham, United Kingdom, (1967)
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The Normalized Matching Property in Random and Pseudorandom Bipartite Graphs
Random bipartite graphs G(k,n,p) have the normalized matching property with a sharp threshold at p = log n / k, and Thomason pseudorandom bipartite graphs admit the property after deletion of a vanishingly small vertex set.