• Computer Science, Mathematics
  • Published in J. Graph Algorithms Appl. 2014
  • DOI:10.7155/jgaa.00357

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

@article{Elbassioni2014APD,
  title={A Polynomial Delay Algorithm for Generating Connected Induced Subgraphs of a Given Cardinality},
  author={Khaled M. Elbassioni},
  journal={J. Graph Algorithms Appl.},
  year={2014},
  volume={19},
  pages={273-280}
}
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 $O((k\min\{(n-k),k\Delta\})^2(\Delta+\log k))$ and uses linear space $O(n+m)$, where $n$ and $m$ are respectively the number of vertices and edges of $G$ and $\Delta$ is the maximum degree. 
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