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International Symposium on Algorithms and Computation

ISAAC 2012: Algorithms and Computation pp 413–422Cite as

On the Number of Upward Planar Orientations of Maximal Planar Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7676))

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 that n-vertex maximal planar graphs have at least Ω(n ·1.189n) and at most O(n ·4n) upward planar orientations. Moreover, there exist n-vertex maximal planar graphs having as few as O(n ·2n) upward planar orientations and n-vertex maximal planar graphs having Ω(2.599n) upward planar orientations.

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Author information

Authors and Affiliations

  1. School of Information Technologies, The University of Sydney, Australia

    Fabrizio Frati & Joachim Gudmundsson

  2. Institute of Theoretical Computer Science, ETH Zurich, Switzerland

    Emo Welzl

Authors
  1. Fabrizio Frati
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  2. Joachim Gudmundsson
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  3. Emo Welzl
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

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© 2012 Springer-Verlag Berlin Heidelberg

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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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  • DOI: https://doi.org/10.1007/978-3-642-35261-4_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35260-7

  • Online ISBN: 978-3-642-35261-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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