Abstract
We investigate connected proper interval graphs without vertex labels. We first give the number of connected proper interval graphs of n vertices. Using it, 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 the reverse search, and it outputs each connected proper interval graph in \(\mbox{\cal O}(1)\) time.
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Saitoh, T., Yamanaka, K., Kiyomi, M., Uehara, R. (2009). Random Generation and Enumeration of Proper Interval Graphs. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_16
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DOI: https://doi.org/10.1007/978-3-642-00202-1_16
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