On the Isolated Vertices and Connectivity in Random Intersection Graphs

الملخص EN

We study isolated vertices and connectivity in the random intersection graph G(n,m,p).

A Poisson convergence for the number of isolated vertices is determined at the threshold for absence of isolated vertices, which is equivalent to the threshold for connectivity.

When m=⌊nα⌋ and α>6, we give the asymptotic probability of connectivity at the threshold for connectivity.

Analogous results are well known in Erdős-Rényi random graphs.