IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/vyid10.1007_s10878-020-00541-z.html
   My bibliography  Save this article

Computation and algorithm for the minimum k-edge-connectivity of graphs

Author

Listed:
  • Yuefang Sun

    (Ningbo University
    Shaoxing University)

  • Chenchen Wu

    (Tianjin University of Technology)

  • Xiaoyan Zhang

    (Nanjing Normal University)

  • Zhao Zhang

    (Zhejiang Normal University)

Abstract

Boesch and Chen (SIAM J Appl Math 34:657–665, 1978) introduced the cut-version of the generalized edge-connectivity, named k-edge-connectivity. For any integer k with $$2\le k\le n$$2≤k≤n, the k-edge-connectivity of a graph G, denoted by $$\lambda _k(G)$$λk(G), is defined as the smallest number of edges whose removal from G produces a graph with at least k components. In this paper, we first compute some exact values and sharp bounds for $$\lambda _k(G)$$λk(G) in terms of n and k. We then discuss the relationships between $$\lambda _k(G)$$λk(G) and other generalized connectivities. An algorithm in $$\mathcal {O}(n^2)$$O(n2) time will be provided such that we can compute a sharp upper bound in terms of the maximum degree. Among our results, we also compute some exact values and sharp bounds for the function f(n, k, t) which is defined as the minimum size of a connected graph G with order n and $$\lambda _k(G)=t$$λk(G)=t.

Suggested Citation

  • Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 0. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00541-z
    DOI: 10.1007/s10878-020-00541-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-020-00541-z
    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/s10878-020-00541-z?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. Lily Chen & Xueliang Li & Mengmeng Liu & Yaping Mao, 2017. "A solution to a conjecture on the generalized connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 275-282, January.
    2. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
    3. Yuefang Sun & Xueliang Li, 2017. "On the difference of two generalized connectivities of a graph," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 283-291, January.
    Full references (including those not matched with items on IDEAS)

    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. Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 2022. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1741-1752, October.
    2. Mark Velednitsky & Dorit S. Hochbaum, 0. "Isolation branching: a branch and bound algorithm for the k-terminal cut problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-21.
    3. Mark Velednitsky & Dorit S. Hochbaum, 2022. "Isolation branching: a branch and bound algorithm for the k-terminal cut problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1659-1679, October.
    4. Mourad Baïou & Francisco Barahona & Ali Ridha Mahjoub, 2000. "Separation of Partition Inequalities," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 243-254, May.
    5. Li, Hengzhe & Wang, Jiajia, 2018. "The λ3-connectivity and κ3-connectivity of recursive circulants," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 750-757.
    6. Yan T. Yang & Barak Fishbain & Dorit S. Hochbaum & Eric B. Norman & Erik Swanberg, 2014. "The Supervised Normalized Cut Method for Detecting, Classifying, and Identifying Special Nuclear Materials," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 45-58, February.
    7. Marie-Christine Costa & Dominique Werra & Christophe Picouleau, 2011. "Minimum d-blockers and d-transversals in graphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 857-872, November.
    8. Costa, Marie-Christine & Letocart, Lucas & Roupin, Frederic, 2005. "Minimal multicut and maximal integer multiflow: A survey," European Journal of Operational Research, Elsevier, vol. 162(1), pages 55-69, April.
    9. Dmitry Krushinsky & Boris Goldengorin, 2012. "An exact model for cell formation in group technology," Computational Management Science, Springer, vol. 9(3), pages 323-338, August.
    10. Hiroshi Nagamochi & Shigeki Katayama & Toshihide Ibaraki, 2000. "A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 151-169, June.
    11. Alena Otto & Erwin Pesch, 2017. "Operation of shunting yards: train-to-yard assignment problem," Journal of Business Economics, Springer, vol. 87(4), pages 465-486, May.
    12. Li, Xiaowang & Zhou, Shuming & Ren, Xiangyu & Guo, Xia, 2021. "Structure and substructure connectivity of alternating group graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).

    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::y::i::d:10.1007_s10878-020-00541-z. 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.