Approximating the Crossing Number of Apex Graphs

  • Markus Chimani
  • Petr Hliněný
  • Petra Mutzel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5417)


We show that the crossing number of an apex graph, i.e. a graph G from which only one vertex v has to be removed to make it planar, can be approximated up to a factor of Δ(G − vd(v)/2 by solving the vertex inserting problem, i.e. inserting a vertex plus incident edges into an optimally chosen planar embedding of a planar graph. Due to a recently developed polynomial algorithm for the latter problem, this establishes the first polynomial fixed-constant approximation algorithm for the crossing number problem of apex graphs with bounded degree.


Crossing number apex graph vertex insertion 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Markus Chimani
    • 1
  • Petr Hliněný
    • 2
  • Petra Mutzel
    • 1
  1. 1.Faculty of CSDortmund University of TechnologyGermany
  2. 2.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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