An efficient algorithm for generating colored outerplanar graphs

Authors:
Jiexun Wang;Liang Zhao;Hiroshi Nagamochi;Tatsuya Akutsu
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan;Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto, Japan
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

Given two integers n and m with 1 ≤ m ≤ n, we consider the problem of generating nonisomorphic colored outerplanar graphs with at most n vertices, where each outerplanar graph is colored with at most m colors. In this paper, we treat outerplanar graphs as rooted outerplane graphs, i.e., plane embeddings with a designated vertex as the root, and propose an efficient algorithm for generating all such colored graphs based on a unique representation of those embeddings. Our algorithm runs in O(n) space and outputs all colored and rooted outerplane graphs without repetition in O(1) time per graph.