No abstract

When the random intersection graph G n m p proposed by Karoński, Scheinerman, and Singer-Cohen [Combin Probab Comput 8 (1999), 131-159] is compared with the independent-edge G n p , the evolutions are different under some values of m and equivalent under others. In particular, when m = n α and α > 6, the total variation distance between the graph random variables has limit 0.

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.

No abstract