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Straight-Line Drawability of a Planar Graph Plus an Edge

  • Peter Eades
  • Seok-Hee HongEmail author
  • Giuseppe Liotta
  • Naoki Katoh
  • Sheung-Hung Poon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

Abstract

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing.

Keywords

Hamilton Path External Face Clockwise Order Edge Crossing Closed Walk 
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 Switzerland 2015

Authors and Affiliations

  • Peter Eades
    • 1
  • Seok-Hee Hong
    • 1
    Email author
  • Giuseppe Liotta
    • 2
  • Naoki Katoh
    • 3
  • Sheung-Hung Poon
    • 4
  1. 1.University of SydneySydneyAustralia
  2. 2.University of PerugiaPerugiaItaly
  3. 3.Kwansei Gakuin UniversityNishinomiyaJapan
  4. 4.Institut Teknologi BruneiGadongBrunei

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