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

  • Md. Jawaherul Alam
  • Franz J. Brandenburg
  • Stephen G. Kobourov
Conference paper

DOI: 10.1007/978-3-319-03841-4_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)
Cite this paper as:
Alam M.J., Brandenburg F.J., Kobourov S.G. (2013) Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs. In: Wismath S., Wolff A. (eds) Graph Drawing. GD 2013. Lecture Notes in Computer Science, vol 8242. Springer, Cham

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.

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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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