Note on k-planar crossing numbers

@article{Pach2018NoteOK,
  title={Note on k-planar crossing numbers},
  author={J. Pach and L. Sz{\'e}kely and Csaba D. T{\'o}th and G. T{\'o}th},
  journal={Comput. Geom.},
  year={2018},
  volume={68},
  pages={2-6}
}
  • J. Pach, L. Székely, +1 author G. Tóth
  • Published 2018
  • Mathematics, Computer Science
  • Comput. Geom.
  • Abstract The crossing number CR ( G ) of a graph G = ( V , E ) is the smallest number of edge crossings over all drawings of G in the plane. For any k ≥ 1 , the k-planar crossing number of G, CR k ( G ) , is defined as the minimum of CR ( G 0 ) + CR ( G 1 ) + … + CR ( G k − 1 ) over all graphs G 0 , G 1 , … , G k − 1 with ∪ i = 0 k − 1 G i = G . It is shown that for every k ≥ 1 , we have CR k ( G ) ≤ ( 2 k 2 − 1 k 3 ) CR ( G ) . This bound does not remain true if we replace the constant 2 k 2… CONTINUE READING

    Topics from this paper.

    New Bounds on k-Planar Crossing Numbers
    On the k-planar local crossing number
    2
    On the 2-colored crossing number
    Approximating the Rectilinear Crossing Number
    11
    Midrange crossing constants for graphs classes
    1
    Using Block Designs in Crossing Number Bounds.
    2
    Some remarks on the midrange crossing constant
    Approximating the rectilinear crossing number
    2

    References

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