Induced subgraphs in sparse random graphs with given degree sequence

Abstract

For any $S\subset [n]$, we compute the probability that the subgraph of ${\mathcal{G}}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is further extended to ${\mathcal{G}}_{\mathbf{d}}$, the probability space of random graphs with a given degree sequence $\mathbf{d}$.

31 pages, 11 figures