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

  • Authors:

  • Katarzyna Rybarczyk

  • Affiliations:

  • Faculty of Mathematics and Computer Science, Department of Discrete Mathematics, Adam Mickiewicz University, 60–769 Poznań, Poland

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2011

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Abstract

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,p̂) 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.