Bounds and Methods for k-Planar Crossing Numbers

  • Farhad Shahrokhi
  • Ondrej Sýkora
  • Laszlo A. Székely
  • Imrich Vrt’o
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number of K2 k + 1, q, for k ≥ 2. We prove tight bounds for complete graphs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Farhad Shahrokhi
    • 1
  • Ondrej Sýkora
    • 2
  • Laszlo A. Székely
    • 3
  • Imrich Vrt’o
    • 4
  1. 1.Department of Computer ScienceUniversity of North TexasDentonUSA
  2. 2.Department of Computer ScienceLoughborough University LoughboroughLeicestershireThe United Kingdom
  3. 3.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  4. 4.Department of InformaticsInstitute of Mathematics Slovak Academy of SciencesBratislavaSlovak Republic

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