On Random Intersection Graphs: The Subgraph Problem

Authors:
Michał Karoński;Edward R. Scheinerman;Karen B. Singer-Cohen
Affiliations:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznán, Poland and Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA (e-mail: k ...;Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218–2689, USA (e-mail: ers@cs.jhu.edu);Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218--2689, USA and School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA (e-mail: singer@mat ...
Venue:
Combinatorics, Probability and Computing
Year:
1999

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Abstract

A new model of random graphs – random intersection graphs – is introduced. In this model, vertices are assigned random subsets of a given set. Two vertices are adjacent provided their assigned sets intersect. We explore the evolution of random intersection graphs by studying thresholds for the appearance and disappearance of small induced subgraphs. An application to gate matrix circuit design is presented.