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Abstract
We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show thatn-vertex maximal planar graphs have at least Ω(n ·1.189n) and at mostO(n ·4n) upward planar orientations. Moreover, there existn-vertex maximal planar graphs having as few asO(n ·2n) upward planar orientations andn-vertex maximal planar graphs having Ω(2.599n) upward planar orientations.
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Authors and Affiliations
School of Information Technologies, The University of Sydney, Australia
Fabrizio Frati & Joachim Gudmundsson
Institute of Theoretical Computer Science, ETH Zurich, Switzerland
Emo Welzl
- Fabrizio Frati
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- Joachim Gudmundsson
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Editors and Affiliations
Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan
Kun-Mao Chao
Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan
Tsan-sheng Hsu
Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan
Der-Tsai Lee
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Frati, F., Gudmundsson, J., Welzl, E. (2012). On the Number of Upward Planar Orientations of Maximal Planar Graphs. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_44
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