Subgraph probability of random graphs with specified degrees and applications to chromatic number and connectivity

Pu Gao, Yuval Ohapkin

Given a graphical degree sequence $\mathbf{d}=(d_1,\dots ,d_n)$, let $G(n,\mathbf{d})$ denote a uniformly random graph on vertex set $[n]$ where vertex $i$ has degree $d_i$ for every…