A Polynomial Delay Algorithm for Generating Connected Induced Subgraphs of a Given Cardinality

We give a polynomial delay algorithm, that for any graph $G$ and positive integer $k$, enumerates all connected induced subgraphs of $G$ of order $k$. Our algorithm enumerates each subgraph in at most $O((k\min \{(n-k),k\mathrm{\Delta }\}{)}^2(\mathrm{\Delta }+\log k))$ and uses linear space $O(n+m)$, where $n$ and $m$ are respectively the number of vertices and edges of $G$ and $\mathrm{\Delta }$ is the maximum degree.