IDEAS home Printed from https://ideas.repec.org/a/ids/ijmore/v2y2010i3p259-289.html
   My bibliography  Save this article

Linear programming formulation of the vertex colouring problem

Author

Listed:
  • Moustapha Diaby

Abstract

In this paper, we present a first linear programming (LP) formulation of the vertex colouring problem (VCP). The complexity orders of the number of variables and the number of constraints of the proposed LP are O (δ9·ς3) and O (δ8·ς3), respectively, where δ and ς are the number of vertices and the number of available colours in the VCP instance, respectively. Hence, the proposed model represents a reaffirmation of 'P = NP'. First, we develop a bipartite network flow (BNF) based model of the problem. Then, we use a graph-based modelling framework similar to that of Diaby to develop the proposed LP model. A numerical example is used to illustrate the approach.

Suggested Citation

  • Moustapha Diaby, 2010. "Linear programming formulation of the vertex colouring problem," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 2(3), pages 259-289.
    • Handle: RePEc:ids:ijmore:v:2:y:2010:i:3:p:259-289
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=32718
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Borja Ena & Alberto Gomez & Borja Ponte & Paolo Priore & Diego Diaz, 2022. "Homogeneous grouping of non-prime steel products for online auctions: a case study," Annals of Operations Research, Springer, vol. 315(1), pages 591-621, August.

    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:ids:ijmore:v:2:y:2010:i:3:p:259-289. 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: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=320 .

    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.