k-Quasi-Planar Graphs

  • Andrew Suk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)


A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A topological graph is simple if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy [16] showed that every n-vertex simple k-quasi-planar graph contains at most \(O\left(n(\log n)^{2k-4}\right)\) edges. This upper bound was recently improved (for large k) by Fox and Pach [8] to n(logn) O(logk). In this note, we show that all such graphs contain at most \((n\log^2n )2^{\alpha^{c_k}(n)}\) edges, where α(n) denotes the inverse Ackermann function and c k is a constant that depends only on k.


Absolute Constant Topological Graph Annual Symposium Geometric Graph Crossing Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew Suk
    • 1
  1. 1.School of Basic SciencesÉcole Polytechnique Fédérale de LausanneSwitzerland

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