Equivalence of a random intersection graph and G(n,p)

We solve the conjecture of Fill, Scheinerman and Singer-Cohen (Random Struct Algorithms 16 (2000), 156–176) and show equivalence of sharp threshold functions of a random intersection graph ${\cal g}$ **image** (n,m,p) with m ≥ n3 and a graph G(n,p) with independent edges. Moreover we prove sharper equivalence results under some additional assumptions. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2011 © 2011 Wiley Periodicals, Inc.

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