Drawing Planar Partitions II: HH-Drawings

  • Therese Biedl
  • Michael Kaufmann
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)


Let a planar graph G=(V,E) and a vertex-partition V=AB 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.


Bipartite Graph Planar Graph Dual Graph Planar Partition Eulerian Circuit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Therese Biedl
    • 1
  • Michael Kaufmann
    • 2
  • Petra Mutzel
    • 3
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada
  2. 2.Wilhelm-Schickard Institut für InformatikUniversität TübingenTübingenGermany
  3. 3.Max-Planck-Institut für InformatikIm StadtwaldSaarbrückenGermany

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