Properties of induced subgraphs of random graphs with given degree sequences

In this thesis we study induced subgraphs of uniformly random graphs with given degree sequences. We study the degree sequence of these subgraphs and use this to study their properties. In particular, we focus on the component structure of this induced subgraph. Under certain restrictions, we characterise the threshold for when induced subgraph is connected, or when the subgraph contains a giant component.