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Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs

  • Md. Jawaherul Alam
  • Franz J. Brandenburg
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend. The drawing can be computed in linear time from any given 1-planar embedding of the graph.

Keywords

Outer Face Base Edge Quadratic Size Regular Vertex Convex Drawing 
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 2013

Authors and Affiliations

  • Md. Jawaherul Alam
    • 1
  • Franz J. Brandenburg
    • 2
  • Stephen G. Kobourov
    • 1
  1. 1.Department of Computer ScienceUniversity of ArizonaUSA
  2. 2.University of PassauPassauGermany

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