IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v44y2022i5d10.1007_s10878-022-00893-8.html
   My bibliography  Save this article

Characterizing 3-uniform linear extremal hypergraphs on feedback vertex number

Author

Listed:
  • Zhongzheng Tang

    (School of Science, Beijing University of Posts and Telecommunications)

  • Yucong Tang

    (Nanjing University of Aeronautics and Astronautics
    Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT)

  • Zhuo Diao

    (School of Statistics and Mathematics, Central University of Finance and Economics)

Abstract

Let $$H=(V,E)$$ H = ( V , E ) be a hypergraph with vertex set V and edge set E. $$S\subseteq V$$ S ⊆ V is a feedback vertex set (FVS) of H if $$H\setminus S$$ H \ S has no cycle and $$\tau _c(H)$$ τ c ( H ) denote the minimum cardinality of a FVS of H. Chen et al. [IWOCA,2016] has proven if H is a linear 3-uniform hypergraph with m edges, then $$\tau _c(H)\le m/3$$ τ c ( H ) ≤ m / 3 . In this paper, we furthermore characterize all the extremal hypergraphs with $$\tau _c(H)= m/3$$ τ c ( H ) = m / 3 holds. This result has a direct application to Tuza’s conjecture.

Suggested Citation

  • Zhongzheng Tang & Yucong Tang & Zhuo Diao, 2022. "Characterizing 3-uniform linear extremal hypergraphs on feedback vertex number," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3310-3330, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00893-8
    DOI: 10.1007/s10878-022-00893-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-022-00893-8
    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/s10878-022-00893-8?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:44:y:2022:i:5:d:10.1007_s10878-022-00893-8. 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.