The “classical” random graph models, in particular G(n,p), are “homogeneous,” in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the… Expand

This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.Expand

We consider a random graph process in which vertices are
added to the graph one at a time and joined to a fixed number
m of earlier vertices, where
each earlier vertex is chosen with probability… Expand

Here the authors obtain P(d) asymptotically for all d≤n1/15, where n is the number of vertices, proving as a consequence that γ=3.9±0.1 is obtained.Expand