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Testing Maximal 1-Planarity of Graphs with a Rotation System in Linear Time

(Extended Abstract)
  • Peter Eades
  • Seok-Hee Hong
  • Naoki Katoh
  • Giuseppe Liotta
  • Pascal Schweitzer
  • Yusuke Suzuki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. A 1-planar embedding of a graph G is maximal if no edge can be added without violating the 1-planarity of G. In this paper we show that the problem of testing maximal 1-planarity of a graph G can be solved in linear time, if a rotation system (i.e., the circular ordering of edges for each vertex) is given. We also prove that there is at most one maximal 1-planar embedding of G that preserves the given rotation system, and our algorithm produces such an embedding in linear time, if it exists.

Keywords

Linear Time Rotation System Linear Time Algorithm Blue Edge Embed 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-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Peter Eades
    • 1
  • Seok-Hee Hong
    • 1
  • Naoki Katoh
    • 2
  • Giuseppe Liotta
    • 3
  • Pascal Schweitzer
    • 4
  • Yusuke Suzuki
    • 5
  1. 1.University of SydneyAustralia
  2. 2.Kyoto UniversityJapan
  3. 3.Universitá di PerugiaItaly
  4. 4.Australian National UniversityAustralia
  5. 5.Niigata UniversityJapan

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