IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v32y2016i3d10.1007_s10878-015-9900-z.html
   My bibliography  Save this article

First-Fit colorings of graphs with no cycles of a prescribed even length

Author

Listed:
  • Manouchehr Zaker

    (Institute for Advanced Studies in Basic Sciences)

  • Hossein Soltani

    (Institute for Advanced Studies in Basic Sciences)

Abstract

The First-Fit (or Grundy) chromatic number of a graph G denoted by $$\chi _{{_\mathsf{FF}}}(G)$$ χ FF ( G ) , is the maximum number of colors used by the First-Fit (greedy) coloring algorithm when applied to G. In this paper we first show that any graph G contains a bipartite subgraph of Grundy number $$\lfloor \chi _{{_\mathsf{FF}}}(G) /2 \rfloor +1$$ ⌊ χ FF ( G ) / 2 ⌋ + 1 . Using this result we prove that for every $$t\ge 2$$ t ≥ 2 there exists a real number $$c>0$$ c > 0 such that in every graph G on n vertices and without cycles of length 2t, any First-Fit coloring of G uses at most $$cn^{1/t}$$ c n 1 / t colors. It is noted that for $$t=2$$ t = 2 this bound is the best possible. A compactness conjecture is also proposed concerning the First-Fit chromatic number involving the even girth of graphs.

Suggested Citation

  • Manouchehr Zaker & Hossein Soltani, 2016. "First-Fit colorings of graphs with no cycles of a prescribed even length," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 775-783, October.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9900-z
    DOI: 10.1007/s10878-015-9900-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9900-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-015-9900-z?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.

    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:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9900-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.