Crossing Numbers and Parameterized Complexity

  • Michael J. Pelsmajer
  • Marcus Schaefer
  • Daniel Štefankovič
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the odd crossing number of G that uses at most 9k crossings, where k is the odd crossing number of G. As a consequence of this and a result of Grohe we can show that the odd crossing number is fixed-parameter tractable.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael J. Pelsmajer
    • 1
  • Marcus Schaefer
    • 2
  • Daniel Štefankovič
    • 3
  1. 1.Illinois Institute of TechnologyChicagoUSA
  2. 2.DePaul UniversityChicagoUSA
  3. 3.University of RochesterRochesterUSA

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