Keith Frankston, Rutgers University

Abstract

The Erdős Rényi random graph (denoted Gn,p) is a random object on n vertices where each edge appears independently with probability p. We call a graph rigid if it has no non-trivial automorphisms. A classical result in random graph theory states that the probability that Gn,p is rigid goes to 1 (as n goes to infinity) for p(1-p)>>log(n)/n. In this talk we discuss what happens when we instead at look at induced subgraphs of Gn,p. We will show that almost surely any induced subgraph of sufficient size is rigid by proving a more general result.