IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v13y2007i2d10.1007_s10878-006-9018-4.html
   My bibliography  Save this article

Fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges

Author

Listed:
  • Sun-Yuan Hsieh

    (National Cheng Kung University)

  • Pei-Yu Yu

    (National Cheng Kung University)

Abstract

Two Hamiltonian paths are said to be fully independent if the ith vertices of both paths are distinct for all i between 1 and n, where n is the number of vertices of the given graph. Hamiltonian paths in a set are said to be mutually fully independent if two arbitrary Hamiltonian paths in the set are fully independent. On the other hand, two Hamiltonian cycles are independent starting at v if both cycles start at a common vertex v and the ith vertices of both cycles are distinct for all i between 2 and n. Hamiltonian cycles in a set are said to be mutually independent starting at v if any two different cycles in the set are independent starting at v. The n-dimensional hypercube is widely used as the architecture for parallel machines. In this paper, we study its fault-tolerant property and show that an n-dimensional hypercube with at most n−2 faulty edges can embed a set of fault-free mutually fully independent Hamiltonian paths between two adjacent vertices, and can embed a set of fault-free mutually independent Hamiltonian cycles starting at a given vertex. The number of tolerable faulty edges is optimal with respect to a worst case.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:2:d:10.1007_s10878-006-9018-4
    DOI: 10.1007/s10878-006-9018-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-006-9018-4
    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/s10878-006-9018-4?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. Sheng-Chyang Liaw & Gerard J. Chang, 1998. "Generalized Diameters and Rabin Numbers of Networks," Journal of Combinatorial Optimization, Springer, vol. 2(4), pages 371-384, December.
    2. Jun-Ming Xu, 2004. "Wide Diameters of Cartesian Product Graphs and Digraphs," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 171-181, June.
    3. Peng-Jun Wan, 1997. "Near-Optimal Conflict-Free Channel Set Assignments for an Optical Cluster-Based Hypercube Network," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 179-186, June.
    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. 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. 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.
    3. 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.
    4. 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.

    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. Yuehua Bu & Xubo Zhu, 2012. "An optimal square coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 580-592, November.
    2. Chitra Balasubramaniam & Sergiy Butenko, 2017. "On robust clusters of minimum cardinality in networks," Annals of Operations Research, Springer, vol. 249(1), pages 17-37, February.

    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:13:y:2007:i:2:d:10.1007_s10878-006-9018-4. 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.