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An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation

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STACS 2003 (STACS 2003)

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Abstract

We propose a new linear time algorithm to represent a planar graph. Based on a specific triangulation of the graph, our coding takes on average 5.03 bits per node, and 3.37 bits per node if the graph is maximal. We derive from this representation that the number of unlabeled planar graphs with n nodes is at most 2∞n+O(log n), where ∞≈5.007. The current lower bound is 2βn+ø(log n) for β≈4.71. We also show that almost all unlabeled and almost all labeled n-node planar graphs have at least 1.70n edges and at most 2.54n edges.

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux I, France

    Nicolas Bonichon, Cyril Gavoille & Nicolas Hanusse

Authors
  1. Nicolas Bonichon
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  2. Cyril Gavoille
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  3. Nicolas Hanusse
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

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Bonichon, N., Gavoille, C., Hanusse, N. (2003). An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_44

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  • DOI: https://doi.org/10.1007/3-540-36494-3_44

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  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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