What is The Probability That A Random Graph With A Given Degree Sequence is Connected?

Louigi Addario-Berry, Bruce Reed, Dao Chen Yuan

An $n$-tuple $D=(d(1),\dots ,d(n))$ is a \emph{feasible degree sequence} if there is a graph on $\{1,\dots ,n\}$ such that $i$ has degree $d(i)$. Any such graph will have $m=\sum_{i=…