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.
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References
Akutsu, T., Fukagawa, D.: Inferring a graph from path frequency. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 371–382. Springer, Heidelberg (2005)
Akutsu, T., Fukagawa, D.: On inference of a chemical structure from path frequency. In: Proc. 2005 International Joint Conference of InCoB, AASBi and KSBI, pp. 96–100 (2005)
Fujiwara, H., et al.: Enumerating tree-like chemical structures from feature vector (in preparation)
Horváth, T., Akutsu, T., Wrobel, S.: A refinement operator for outerplanar graphs. In: Proc. 16th International Conference of Inductive Logic Programming, pp. 95–97 (2006)
Li, G., Ruskey, F.: The advantage of forward thinking in generating rooted and free trees. In: Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 939–940 (1999)
Nagamochi, H.: A detachment algorithm for inferring a graph from path frequency. In: Chen, D.Z., Lee, D.T. (eds.) COCOON 2006. LNCS, vol. 4112, pp. 274–283. Springer, Heidelberg (2006)
Nakano, S., Uno, T.: Efficient generation of rooted trees, NII Technical Report (NII-2003-005) (2003), http://research.nii.ac.jp/TechReports/03-005E.html
Nakano, S., Uno, T.: Generating colored trees. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 249–260. Springer, Heidelberg (2005)
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Wang, J., Zhao, L., Nagamochi, H., Akutsu, T. (2007). An Efficient Algorithm for Generating Colored Outerplanar Graphs. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_52
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DOI: https://doi.org/10.1007/978-3-540-72504-6_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72503-9
Online ISBN: 978-3-540-72504-6
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