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DTSTART:20260329T010000
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DTSTART;TZID=Europe/Paris:20260413T110000
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DTSTAMP:20260413T014424
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SUMMARY:Serte Donderwinkel - Counting connected graphs
DESCRIPTION:How many connected graphs have a prescribed degree sequence?This classical combinatorial question turns out to admit a natural probabilistic approach. \nIn 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. \nConcretely\, we construct a random graph in which (an approximation of) the prescribed degree sequence appears with high probability inside a large connected component. This perspective allows us to translate questions about enumeration into probabilistic statements about random graphs. \nAlong the way\, I will discuss several key probabilistic tools\, including the configuration model\, branching process approximations\, and local weak convergence\, and explain how they combine to yield asymptotic counting results.
URL:https://www.math.ens.psl.eu/evenement/serte-donderwinkel-counting-connected-graphs/
LOCATION:Salle W (ENS)
CATEGORIES:Séminaire informel de probabilités
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