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

A method by Hoeffding is used to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure and applications are given to U -statistics, random strings and random graphs.Expand

A “uniform” model of random graphs, which allows self-loops and multiple edges, is shown to lead to formulas that are substanitially simpler than the analogous formulas for the classical random graphs of Erdos and Renyi.Expand

Abstract.We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic… Expand

It is shown that, asymptotically for a sequence of such multigraphs with the number of edges $\tfrac12\sumd\to\infty$, the probability that the multigraph is simple stays away from 0 if and only if $\sumdd=O bigpar{\sumd}$.Expand

The asymptotic distribution of the number of Hamilton cycles in a random regular graph is determined, and results imply that some different models of random regular graphs are contiguous, which means that they are qualitatively asymPTotically equivalent.Expand

LetG be a fixed graph and letXG be the number of copies ofG contained in the random graphG(n, p). We prove exponential bounds on the upper tail ofXG which are best possible up to a logarithmic factor… Expand