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Drawing Planar Partitions II: HH-Drawings

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Graph-Theoretic Concepts in Computer Science (WG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1517))

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Abstract

Let a planar graph G=(V,E) and a vertex-partition V=A ∪ B be given. Can we draw G without edge crossings such that the partition is clearly visible? Such drawings aid to display partitions and cuts as they arise in various applications. In this paper, we study planar drawings of G in which the vertex classes A and B are separated by a horizontal line (so-called HH-drawings). We provide necessary and sufficient conditions for the existence of so-called y-monotone planar HH-drawings, and a linear time algorithm to construct, if possible, a y-monotone planar HH-drawing of area \({\cal O}(\vert V\vert^2)\) with few bends. Furthermore, we give an exponential lower bound for the area of straight-line planar HH-drawings. Finally, we study planar HH-drawings that are not y-monotone.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, 3480 University St., Montréal, Québec, H3A2A7, Canada

    Therese Biedl

  2. Wilhelm-Schickard Institut für Informatik, Universität Tübingen, D-72116, Tübingen, Germany

    Michael Kaufmann

  3. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Petra Mutzel

Authors
  1. Therese Biedl
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  2. Michael Kaufmann
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  3. Petra Mutzel
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Editor information

Editors and Affiliations

  1. Department of Computer Science, ETH Zurich, ETH Zentrum, CH-8022, Zurich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, University of Loughborough, Loughborough, UK

    Ondrej Sýkora

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© 1998 Springer-Verlag Berlin Heidelberg

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Biedl, T., Kaufmann, M., Mutzel, P. (1998). Drawing Planar Partitions II: HH-Drawings. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_11

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  • DOI: https://doi.org/10.1007/10692760_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65195-6

  • Online ISBN: 978-3-540-49494-2

  • eBook Packages: Springer Book Archive

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