Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph

Anita Liebenau, Nick Wormald

Published 2017-02-27Version 1

In this paper we derive a result that establishes the validity of a model for a basic parameter of a random graph, its degree sequence. Simultaneously, the result gives an asymptotic formula for the number of graphs with given degree sequence, which is also of fundamental importance. The results verify two conjectures of McKay and Wormald made in 1990 and 1997.