IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v24y2012i1d10.1007_s10878-010-9290-1.html
   My bibliography  Save this article

Max-coloring paths: tight bounds and extensions

Author

Listed:
  • Telikepalli Kavitha

    (Indian Institute of Science)

  • Julián Mestre

    (Max-Plank-Institut für Informatik)

Abstract

The max-coloring problem is to compute a legal coloring of the vertices of a graph G=(V,E) with vertex weights w such that $\sum_{i=1}^{k}\max_{v\in C_{i}}w(v_{i})$ is minimized, where C 1,…,C k are the various color classes. For general graphs, max-coloring is as hard as the classical vertex coloring problem, a special case of the former where vertices have unit weight. In fact, in some cases it can even be harder: for example, no polynomial time algorithm is known for max-coloring trees. In this paper we consider the problem of max-coloring paths and its generalization, max-coloring skinny trees, a broad class of trees that includes paths and spiders. For these graphs, we show that max-coloring can be solved in time O(|V|+time for sorting the vertex weights). When vertex weights are real numbers, we show a matching lower bound of Ω(|V|log |V|) in the algebraic computation tree model.

Suggested Citation

  • Telikepalli Kavitha & Julián Mestre, 2012. "Max-coloring paths: tight bounds and extensions," Journal of Combinatorial Optimization, Springer, vol. 24(1), pages 1-14, July.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:1:d:10.1007_s10878-010-9290-1
    DOI: 10.1007/s10878-010-9290-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-010-9290-1
    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/s10878-010-9290-1?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:24:y:2012:i:1:d:10.1007_s10878-010-9290-1. 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.