IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/2071887.html
   My bibliography  Save this article

The χ-Boundedness of P2∪P3-Free Graphs

Author

Listed:
  • Xiao Wang
  • Donghan Zhang
  • Serkan Araci

Abstract

In the early 1980s, Gyárfás introduced the concept of the χ-bound with χ-binding functions thereby extending the notion of perfectness. There are a number of challenging conjectures about the χ-bound. Let χG, ωG, and ΔG be the chromatic number, clique number, and maximum degree of a graph G, respectively. In this paper, we prove that if G is a triangle-free and P2∪P3-free graph, then χG≤3 unless G is one of eight graphs with ΔG=5 and χG=4, where the eight graphs are extended from the Grötzsch graph as a Mycielskian of a 5-cycle graph. Moreover, we also show that χG≤3ωG if G is a P2∪P3,W4-free graph.

Suggested Citation

  • Xiao Wang & Donghan Zhang & Serkan Araci, 2022. "The χ-Boundedness of P2∪P3-Free Graphs," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, June.
    • Handle: RePEc:hin:jjmath:2071887
    DOI: 10.1155/2022/2071887
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/jmath/2022/2071887.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/jmath/2022/2071887.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2071887?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:hin:jjmath:2071887. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.