IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v116y2002i1p71-7710.1023-a1021363810398.html
   My bibliography  Save this article

On Clique-Transversals and Clique-Independent Sets

Author

Listed:
  • Guillermo Durán
  • Min Lin
  • Jayme Szwarcfiter

Abstract

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by τ C (G) and α C (G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when τ C (H)=α C (H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters τ C (G) and α C (G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference τ C (G)−α C (G) is arbitrarily large. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Guillermo Durán & Min Lin & Jayme Szwarcfiter, 2002. "On Clique-Transversals and Clique-Independent Sets," Annals of Operations Research, Springer, vol. 116(1), pages 71-77, October.
    • Handle: RePEc:spr:annopr:v:116:y:2002:i:1:p:71-77:10.1023/a:1021363810398
    DOI: 10.1023/A:1021363810398
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/A:1021363810398
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1023/A:1021363810398?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.

    Citations

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


    Cited by:

    1. Hine, Julian & Grieco, Margaret, 2003. "Scatters and clusters in time and space: implications for delivering integrated and inclusive transport," Transport Policy, Elsevier, vol. 10(4), pages 299-306, October.
    2. Chuan-Min Lee, 2010. "Variations of maximum-clique transversal sets on graphs," Annals of Operations Research, Springer, vol. 181(1), pages 21-66, December.
    3. Ke Liu & Mei Lu, 2021. "Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 923-933, May.
    4. Zuosong Liang & Erfang Shan & Liying Kang, 2019. "The clique-perfectness and clique-coloring of outer-planar graphs," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 794-807, October.
    5. Guillermo Durán & Min Lin & Sergio Mera & Jayme Szwarcfiter, 2008. "Algorithms for finding clique-transversals of graphs," Annals of Operations Research, Springer, vol. 157(1), pages 37-45, January.

    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:annopr:v:116:y:2002:i:1:p:71-77:10.1023/a:1021363810398. 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.