Random Generation and Enumeration of Proper Interval Graphs

Authors:
Toshiki Saitoh;Katsuhisa Yamanaka;Masashi Kiyomi;Ryuhei Uehara
Affiliations:
School of Information Science, JAIST, Ishikawa, Japan 923-1292;Graduate School of Information Systems, The University of Electro-Communications, Tokyo, Japan 182-8585;School of Information Science, JAIST, Ishikawa, Japan 923-1292;School of Information Science, JAIST, Ishikawa, Japan 923-1292
Venue:
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Year:
2009

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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.