IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v41y2021i4d10.1007_s10878-021-00703-7.html
   My bibliography  Save this article

Complete-Subgraph-Transversal-Sets problem on bounded treewidth graphs

Author

Listed:
  • Ke Liu

    (Tsinghua University)

  • Mei Lu

    (Tsinghua University)

Abstract

Let $$G=(V,E)$$ G = ( V , E ) be a graph. A complete subgraph of G is a subgraph of pairwise adjacent vertices of V of size at least 2. Let $$\Phi _C(G)$$ Φ C ( G ) be the set of all complete subgraphs of G and $$\Phi \subseteq {\Phi }_C(G)$$ Φ ⊆ Φ C ( G ) . In this paper, we consider the Complete-Subgraph-Transversal-Set on $$\Phi $$ Φ problem and the L-Max Complete-Subgraph-Transversal-Set on $$\Phi $$ Φ problem. We give polynomial time algorithms to these two problems on graphs of bounded treewidth. At last, we show the connections between these two problems with some other NP-complete problems, for example Clique-Transversal-Set problem on graphs and Vertex-Cover problem on hypergraphs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:4:d:10.1007_s10878-021-00703-7
    DOI: 10.1007/s10878-021-00703-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00703-7
    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/s10878-021-00703-7?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.
    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. 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.
    2. 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.
    3. 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.
    4. Chuan-Min Lee, 2010. "Variations of maximum-clique transversal sets on graphs," Annals of Operations Research, Springer, vol. 181(1), pages 21-66, December.

    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:41:y:2021:i:4:d:10.1007_s10878-021-00703-7. 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.