IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v27y2014i2d10.1007_s10878-012-9528-1.html
   My bibliography  Save this article

On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube

Author

Listed:
  • Tzu-Liang Kung

    (Asia University)

  • Cheng-Kuan Lin

    (National Chiao Tung University)

  • Lih-Hsing Hsu

    (Providence University)

Abstract

Hsieh and Yu (2007) first claimed that an injured n-dimensional hypercube Q n contains (n−1−f)-mutually independent fault-free Hamiltonian cycles, where f≤n−2 denotes the total number of permanent edge-faults in Q n for n≥4, and edge-faults can occur everywhere at random. Later, Kueng et al. (2009a) presented a formal proof to validate Hsieh and Yu’s argument. This paper aims to improve this mentioned result by showing that up to (n−f)-mutually independent fault-free Hamiltonian cycles can be embedded under the same condition. Let F denote the set of f faulty edges. If all faulty edges happen to be incident with an identical vertex s, i.e., the minimum degree of the survival graph Q n −F is equal to n−f, then Q n −F contains at most (n−f)-mutually independent Hamiltonian cycles starting from s. From such a point of view, the presented result is optimal. Thus, not only does our improvement increase the number of mutually independent fault-free Hamiltonian cycles by one, but also the optimality can be achieved.

Suggested Citation

  • Tzu-Liang Kung & Cheng-Kuan Lin & Lih-Hsing Hsu, 2014. "On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 328-344, February.
  • Handle: RePEc:spr:jcomop:v:27:y:2014:i:2:d:10.1007_s10878-012-9528-1
    DOI: 10.1007/s10878-012-9528-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9528-1
    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/s10878-012-9528-1?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. Sun-Yuan Hsieh & Pei-Yu Yu, 2007. "Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 153-162, February.
    2. Nelson Castañeda & Ivan S. Gotchev, 2010. "Embedded paths and cycles in faulty hypercubes," Journal of Combinatorial Optimization, Springer, vol. 20(3), pages 224-248, 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. Yingbo Wu & Tianrui Zhang & Shan Chen & Tianhui Wang, 2017. "The Minimum Spectral Radius of an Edge-Removed Network: A Hypercube Perspective," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-8, April.

    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. Gregor, Petr & Škrekovski, Riste & Vukašinović, Vida, 2015. "Rooted level-disjoint partitions of Cartesian products," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 244-258.
    2. Tz-Liang Kueng & Cheng-Kuan Lin & Tyne Liang & Jimmy J. M. Tan & Lih-Hsing Hsu, 2009. "A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges," Journal of Combinatorial Optimization, Springer, vol. 17(3), pages 312-322, April.
    3. Gregor, Petr & Škrekovski, Riste & Vukašinović, Vida, 2018. "Modelling simultaneous broadcasting by level-disjoint partitions," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 15-23.

    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:27:y:2014:i:2:d:10.1007_s10878-012-9528-1. 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.