Sandwiching random graphs: universality between random graph models

Abstract

The goal of this paper is to establish a connection between two classical models of random graphs: the random graph G( n, p) and the random regular graph G d ( n). This connection appears to be very useful in deriving properties of one model from the other and explains why many graph invariants are universal. In particular, one obtains one-line proofs of several highly non-trivial and recent results on G d ( n).