IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v449y2023ics0096300323001339.html
   My bibliography  Save this article

Geodetic convexity and kneser graphs

Author

Listed:
  • Bedo, Marcos
  • Leite, João V.S.
  • Oliveira, Rodolfo A.
  • Protti, Fábio

Abstract

The Kneser graphK(2n+k,n), for n≥1 and k≥0, is the graph G=(V,E) such that V={S⊆{1,…,2n+k}:|S|=n} and there is an edge uv∈E whenever u∩v=∅. Kneser graphs have a nice combinatorial structure, and many parameters have been determined for them, such as the diameter, the chromatic number, the independence number, and, recently, the hull number (in the context of P3-convexity). However, the determination of geodetic convexity parameters in Kneser graphs still remained open. In this work, we investigate both the geodetic number and the geodetic hull number of Kneser graphs. We give upper bounds and determine the exact value of these parameters for Kneser graphs of diameter two (which form a nontrivial subfamily). We prove that the geodetic hull number of a Kneser graph of diameter two is two, except for K(5,2), K(6,2), and K(8,3), which have geodetic hull number three. We also contribute to the knowledge on Kneser graphs by presenting a characterization of endpoints of diametral paths in K(2n+k,n), used as a tool for obtaining some of the main results in this work.

Suggested Citation

  • Bedo, Marcos & Leite, João V.S. & Oliveira, Rodolfo A. & Protti, Fábio, 2023. "Geodetic convexity and kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 449(C).
  • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323001339
    DOI: 10.1016/j.amc.2023.127964
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323001339
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2023.127964?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jin, Zemin & Wang, Fang & Wang, Huaping & Lv, Bihong, 2020. "Rainbow triangles in edge-colored Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    2. Liao, Jiaqi & Cao, Mengyu & Lu, Mei, 2023. "On the P3-hull numbers of q-Kneser graphs and Grassmann graphs," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qin, Zhongmei & Lei, Hui & Li, Shasha, 2020. "Rainbow numbers for small graphs in planar graphs," Applied Mathematics and Computation, Elsevier, vol. 371(C).

    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:eee:apmaco:v:449:y:2023:i:c:s0096300323001339. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.