IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p525-d509492.html
   My bibliography  Save this article

An Improvement of the Lower Bound on the Minimum Number of ≤ k -Edges

Author

Listed:
  • Javier Rodrigo

    (Departamento de Matemática Aplicada, E.T.S.I. Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain)

  • Susana Merchán

    (Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain)

  • Danilo Magistrali

    (Departamento de Matemática Aplicada, E.T.S.I. Universidad Pontificia Comillas, Alberto Aguilera 25, 28015 Madrid, Spain)

  • Mariló López

    (Departamento de Matemática e Informática Aplicadas a las Ingenierías Civil y Naval, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Profesor Aranguren, 3, 28040 Madrid, Spain)

Abstract

In this paper, we improve the lower bound on the minimum number of ≤ k -edges in sets of n points in general position in the plane when k is close to n 2 . As a consequence, we improve the current best lower bound of the rectilinear crossing number of the complete graph K n for some values of n .

Suggested Citation

  • Javier Rodrigo & Susana Merchán & Danilo Magistrali & Mariló López, 2021. "An Improvement of the Lower Bound on the Minimum Number of ≤ k -Edges," Mathematics, MDPI, vol. 9(5), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:525-:d:509492
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/525/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/525/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:525-:d:509492. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.