Random Generation and Enumeration of Proper Interval Graphs

@inproceedings{Saitoh2010RandomGA,
  title={Random Generation and Enumeration of Proper Interval Graphs},
  author={Toshiki Saitoh and Katsuhisa Yamanaka and Masashi Kiyomi and Ryuhei Uehara},
  year={2010}
}
We investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using this result, a simple algorithm that generates a connected proper interval graph uniformly at random up to isomorphism is presented. Finally an enumeration algorithm of connected proper interval graphs is proposed. The algorithm is based on reverse search, and it outputs each connected proper interval graph in O(1) time. 

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