Abstract
In this article we define a canonical decomposition of rooted outerplanar maps into a spanning tree and a list of edges. This decomposition, constructible in linear time, implies the existence of bijection between rooted outerplanar maps with n nodes and bicolored rooted ordered trees with n nodes where all the nodes of the last branch are colored white. As a consequence, for rooted outerplanar maps of n nodes, we derive:
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an enumeration formula, and an asymptotic of 23n − Θ(logn);
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an optimal data structure of asymptotically 3n bits, built in O(n) time, supporting adjacency and degree queries in worst-case constant time;
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an O(n) expected time uniform random generating algorithm.
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Bonichon, N., Gavoille, C., Hanusse, N. (2003). Canonical Decomposition of Outerplanar Maps and Application to Enumeration, Coding, and Generation. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_8
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DOI: https://doi.org/10.1007/978-3-540-39890-5_8
Publisher Name: Springer, Berlin, Heidelberg
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