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Estimating the Growth Constant of Labelled Planar Graphs

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Mathematics and Computer Science III

Part of the book series: Trends in Mathematics ((TM))

Abstract

Let Gn be the number of labelled planar graphs on n vertices and \( \gamma = \lim _{n \to \infty } \left( {G_n /n!} \right)^{1/n} \) .It is known that 26.1848<<30.0606. In this paper we sharpen these bounds to 27.22685<<27.22688. The proof is based on recent results of Bender, Gao and Wormald [Elec. J. Combinatorics 9 (2002) R43], and on singularity analysis of generating functions

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Author information

Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Catalunya, Spain

    Omer Giménez

  2. Universitat Politècnica de Catalunya, Catalunya, Spain

    Marc Noy

Authors
  1. Omer Giménez
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  2. Marc Noy
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Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10, Wien, 1040, Austria

    Michael Drmota  & Bernhard Gittenberger  & 

  2. INRIA Rocquencourt, Le Chesnay, 78153, France

    Philippe Flajolet

  3. PRISM, Université de Versailles-St-Quentin, Bâtiment Descartes 45 avenue des Etats-Unis, Versailles Cedex, 78035, France

    Danièle Gardy

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© 2004 Springer Basel AG

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Giménez, O., Noy, M. (2004). Estimating the Growth Constant of Labelled Planar Graphs. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_12

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  • DOI: https://doi.org/10.1007/978-3-0348-7915-6_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9620-7

  • Online ISBN: 978-3-0348-7915-6

  • eBook Packages: Springer Book Archive

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