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Recursive Generation of 5-Regular Planar Graphs

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WALCOM: Algorithms and Computation (WALCOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5431))

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Abstract

We describe for the first time how the 5-regular simple planar graphs can all be obtained from an elementary family of starting graphs by repeatedly applying a few local expansion operations. The proof uses an innovative amalgam of theory and computation. By incorporating the recursion into the canonical construction path method of isomorph rejection, a generator of non-isomorphic embedded 5-regular planar graphs is obtained with time complexity O(n 2) per isomorphism class.

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Author information

Authors and Affiliations

  1. Department of Computer Science Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

    Mahdieh Hasheminezhad

  2. Department of Computer Science, Australian National University, ACT 0200, Australia

    Brendan D. McKay

  3. Polytopia Systems Pty. Ltd., 19 Colbeck Street, Mawson, ACT, 2607, Australia

    Tristan Reeves

Authors
  1. Mahdieh Hasheminezhad
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  2. Brendan D. McKay
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  3. Tristan Reeves
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Editor information

Editors and Affiliations

  1. Indian Statistical Institute, 700 108, Kolkata, India

    Sandip Das

  2. Japan Advanced Institute of Science and Technology, 923-1292, Ishikawa, Japan

    Ryuhei Uehara

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© 2009 Springer-Verlag Berlin Heidelberg

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Hasheminezhad, M., McKay, B.D., Reeves, T. (2009). Recursive Generation of 5-Regular Planar Graphs. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_12

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  • DOI: https://doi.org/10.1007/978-3-642-00202-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00201-4

  • Online ISBN: 978-3-642-00202-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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