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
Conference paper
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.

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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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