Abstract
Let W 1,…,W n be independent random subsets of [m]={1,…,m}. Assuming that each W i is uniformly distributed in the class of d-subsets of [m] we study the uniform random intersection graph G s (n,m,d) on the vertex set {W 1,…W n }, defined by the adjacency relation: W i ∼W j whenever |W i ∩W j |≧s. For even n we show that as n,m→∞ the edge density threshold for the property that G s (n,m,d) contains a perfect matching is asymptotically the same as that for G s (n,m,d) being connected.
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Bloznelis, M., Łuczak, T. Perfect matchings in random intersection graphs. Acta Math Hung 138, 15–33 (2013). https://doi.org/10.1007/s10474-012-0266-8
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DOI: https://doi.org/10.1007/s10474-012-0266-8