Séminaire de Probabilités commun ICJ/UMPA
# Connectivity Thresholds for graphs with a fixed degree sequence

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Description

We consider the probability space of random graphs with a fixed degree sequence

(the degree of a vertex in a graph is the number of edges incident to it; the degree sequence

specifies the degree of each vertex). We characterize for which degree sequences a uniformly

random graph with the given degree sequence has a giant component (a component with a

constant fraction of the vertices) almost surely. (Joint with Joos, Rautenbach, and Perarnau.)