IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v343y2004icp401-423.html
   My bibliography  Save this article

On the phase transitions of graph coloring and independent sets

Author

Listed:
  • Barbosa, Valmir C.
  • Ferreira, Rubens G.

Abstract

We study combinatorial indicators related to the characteristic phase transitions associated with the optimization problems of coloring the nodes of a graph with the minimum number of colors and of finding an independent set of maximum cardinality in a graph. In particular, we investigate the role of the acyclic orientations of the graph in the hardness of finding the graph's chromatic number and independence number. We provide empirical evidence that, along a sequence of increasingly denser random graphs, the fraction of acyclic orientations that are “shortest” peaks when the chromatic number increases, and that such maxima tend to coincide with locally easiest instances of the problem. Similar evidence is provided concerning the “widest” acyclic orientations and the independence number.

Suggested Citation

  • Barbosa, Valmir C. & Ferreira, Rubens G., 2004. "On the phase transitions of graph coloring and independent sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 401-423.
    • Handle: RePEc:eee:phsmap:v:343:y:2004:i:c:p:401-423
    DOI: 10.1016/j.physa.2004.05.055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104007344
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2004.05.055?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. Valmir C. Barbosa & Carlos A.G. Assis & Josina O. Do Nascimento, 2004. "Two Novel Evolutionary Formulations of the Graph Coloring Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 41-63, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Valmir C Barbosa, 2010. "Network Conduciveness with Application to the Graph-Coloring and Independent-Set Optimization Transitions," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-9, July.

    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. Xiao-Feng Xie & Jiming Liu, 2009. "Graph coloring by multiagent fusion search," Journal of Combinatorial Optimization, Springer, vol. 18(2), pages 99-123, August.
    2. Bernard Gendron & Alain Hertz & Patrick St-Louis, 2007. "On edge orienting methods for graph coloring," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 163-178, February.
    3. Valmir C Barbosa, 2010. "Network Conduciveness with Application to the Graph-Coloring and Independent-Set Optimization Transitions," PLOS ONE, Public Library of Science, vol. 5(7), pages 1-9, July.

    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:phsmap:v:343:y:2004:i:c:p:401-423. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.