I am pleased to announce the following seminar at Milano-Bicocca: Remco van der Hofstad (Eindhoven University of Technology) The number and structure of connected graphs with a fixed degree sequence Friday, 25 September at 14:00 Room U9-08 (Building U9, Viale dell'Innovazione 10, Milano) Streaming (WebEx): link <https://unimib.webex.com/unimib-it/j.php?MTID=m231eb8e5e4a064481de4a585b6bee6c1> The abstract follows below. Everyone interested is welcome. Best regards, Francesco Caravenna %%%%%%%%%%%%%%%%%%%%%%%%%% Abstract. We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs up to a subexponential order. We do this by viewing a connected graph with a given degree distribution as the realization of the giant component in a larger configuration model, and carefully choosing the degree distribution of the larger graph so that it is likely that its giant component has the required degree distribution. To ensure that the connected graph has exactly the correct degrees, we use a switching argument. We further identify the local structure of a uniform random graph with prescribed degrees. This is joint work with Sasha Bell and Serte Donderwinkel. Possibly I will also touch upon work with them and Luisa Andreis. %%%%%%%%%%%%%%%%%%%%%%%%%% -- __________________________________ Francesco Caravenna Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca https://fcaraven.github.io/ __________________________________