# Induced subgraphs in sparse random graphs with given degree sequence - Mathematics > Combinatorics

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 $d=on^{1-3}$ and is further extended to$\mathcal{G} {{\bf d}}$, the probability space of random graphs with a givendegree sequence $\bf d$.

Author: Pu Gao, Yi Su, Nicholas Wormald

Source: https://arxiv.org/