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Spherical-Rectangular Drawings

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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 extend the concept of rectangular drawing to drawings on a sphere using meridians and circles of latitude such that each face is bounded by at most two circles and at most two meridians. This is called spherical-rectangular drawing. Special cases include drawing on a cylinder, a cone, or a lattice of concentric circles on the plane. In this paper, we prove necessary and sufficient conditions for cubic planar graphs to have spherical-rectangular drawings, and show that one can find in linear time a spherical-rectangular drawing of a subcubic planar graph if it has one.

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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 & S. Mehdi Hashemi

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

    Brendan D. McKay

Authors
  1. Mahdieh Hasheminezhad
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  2. S. Mehdi Hashemi
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  3. Brendan D. McKay
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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., Hashemi, S.M., McKay, B.D. (2009). Spherical-Rectangular Drawings. 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_30

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  • DOI: https://doi.org/10.1007/978-3-642-00202-1_30

  • 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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