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The Rectilinear Crossing Number of K n : Closing in (or Are We?)

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Thirty Essays on Geometric Graph Theory

Abstract

The calculation of the rectilinear crossing number of complete graphs is an important open problem in combinatorial geometry, with important and fruitful connections to other classical problems. Our aim in this chapter is to survey the body of knowledge around this parameter.

Mathematics Subject Classification (2010): 52C30, 52C10, 52C45, 05C62, 68R10, 60D05, 52A22

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Notes

  1. 1.

    Aichholzer, personal communication.

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Author information

Authors and Affiliations

  1. Department of Mathematics, California State University at Northridge, Northridge, CA, USA

    Bernardo M. Ábrego & Silvia Fernández-Merchant

  2. Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico

    Gelasio Salazar

Authors
  1. Bernardo M. Ábrego
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  2. Silvia Fernández-Merchant
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  3. Gelasio Salazar
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Corresponding author

Correspondence to Bernardo M. Ábrego .

Editor information

Editors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    János Pach (Chair of Combinatorial Geometry) (Chair of Combinatorial Geometry)

  2. École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    János Pach (Chair of Combinatorial Geometry) (Chair of Combinatorial Geometry)

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Ábrego, B.M., Fernández-Merchant, S., Salazar, G. (2013). The Rectilinear Crossing Number of K n : Closing in (or Are We?). In: Pach, J. (eds) Thirty Essays on Geometric Graph Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0110-0_2

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