Serte Donderwinkel – Counting connected graphs
Salle W (ENS)How many connected graphs have a prescribed degree sequence?This classical combinatorial question turns out to admit a natural probabilistic approach. In joint ongoing work with Sasha Bell and Remco van der Hofstad, we derive asymptotic formulas for the number of connected graphs with a given degree sequence. Our approach is an example of the probabilistic method: rather than counting directly, we introduce a suitable random graph model and study the likelihood that it exhibits a desired structure. Concretely, we construct a random graph in which (an approximation of) the prescribed […]