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1-Bend Upward Planar Drawings of SP-Digraphs

  • Emilio Di Giacomo
  • Giuseppe Liotta
  • Fabrizio MontecchianiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

It is proved that every series-parallel digraph whose maximum vertex-degree is \(\varDelta \) admits an upward planar drawing with at most one bend per edge such that each edge segment has one of \(\varDelta \) distinct slopes. This is shown to be worst-case optimal in terms of the number of slopes. Furthermore, our construction gives rise to drawings with optimal angular resolution \(\frac{\pi }{\varDelta }\). A variant of the proof technique is used to show that (non-directed) reduced series-parallel graphs and flat series-parallel graphs have a (non-upward) one-bend planar drawing with \(\lceil \frac{\varDelta }{2}\rceil \) distinct slopes if biconnected, and with \(\lceil \frac{\varDelta }{2}\rceil +1\) distinct slopes if connected.

Keywords

Planar Graph Decomposition Tree Vertical Segment Horizontal Segment Outerplanar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Giuseppe Liotta
    • 1
  • Fabrizio Montecchiani
    • 1
    Email author
  1. 1.Dip. di IngegneriaUniversità Degli Studi di PerugiaPerugiaItaly

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