IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v181y2010i1p21-6610.1007-s10479-009-0673-6.html
   My bibliography  Save this article

Variations of maximum-clique transversal sets on graphs

Author

Listed:
  • Chuan-Min Lee

Abstract

A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we introduce the concept of maximum-clique perfect and some variations of the maximum-clique transversal set problem such as the {k}-maximum-clique, k-fold maximum-clique, signed maximum-clique, and minus maximum-clique transversal problems. We show that balanced graphs, strongly chordal graphs, and distance-hereditary graphs are maximum-clique perfect. Besides, we present a unified approach to these four problems on strongly chordal graphs and give complexity results for the following classes of graphs: split graphs, balanced graphs, comparability graphs, distance-hereditary graphs, dually chordal graphs, doubly chordal graphs, chordal graphs, planar graphs, and triangle-free graphs. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Chuan-Min Lee, 2010. "Variations of maximum-clique transversal sets on graphs," Annals of Operations Research, Springer, vol. 181(1), pages 21-66, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:21-66:10.1007/s10479-009-0673-6
    DOI: 10.1007/s10479-009-0673-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0673-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0673-6?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. 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.
    2. 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.
    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. Chuan-Min Lee, 2023. "Clique Transversal Variants on Graphs: A Parameterized-Complexity Perspective," Mathematics, MDPI, vol. 11(15), pages 1-33, 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. 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. 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.
    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.

    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:181:y:2010:i:1:p:21-66:10.1007/s10479-009-0673-6. 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: 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.