On Self-Approaching and Increasing-Chord Drawings of 3-Connected Planar Graphs

  • Martin Nöllenburg
  • Roman Prutkin
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)


An st-path in a drawing of a graph is self-approaching if during a traversal of the corresponding curve from s to any point t′ on the curve the distance to t′ is non-increasing. A path has increasing chords if it is self-approaching in both directions. A drawing is self-approaching (increasing-chord) if any pair of vertices is connected by a self-approaching (increasing-chord) path.

We study self-approaching and increasing-chord drawings of triangulations and 3-connected planar graphs. We show that in the Euclidean plane, triangulations admit increasing-chord drawings, and for planar 3-trees we can ensure planarity. Moreover, we give a binary cactus that does not admit a self-approaching drawing. Finally, we show that 3-connected planar graphs admit increasing-chord drawings in the hyperbolic plane and characterize the trees that admit such drawings.


Hyperbolic Plane Graph Drawing Parent Block Plane Triangulation Monotone Path 
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-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Martin Nöllenburg
    • 1
  • Roman Prutkin
    • 1
  • Ignaz Rutter
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyGermany

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