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A solution to a conjecture on the generalized connectivity of graphs

Author

Listed:
  • Lily Chen

    (Huaqiao University
    Nankai University)

  • Xueliang Li

    (Nankai University)

  • Mengmeng Liu

    (Nankai University
    Lanzhou Jiaotong University)

  • Yaping Mao

    (Nankai University
    Qinghai Normal University)

Abstract

The generalized k-connectivity $$\kappa _k(G)$$ κ k ( G ) of a graph G was introduced by Chartrand et al. in (Bull Bombay Math Colloq 2:1–6, 1984), which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we consider the computational complexity of the generalized connectivity and generalized edge-connectivity of a graph. We give a confirmative solution to a conjecture raised by S. Li in Ph.D. Thesis (2012). We also give a polynomial-time algorithm to a problem of generalized k-edge-connectivity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9955-x
    DOI: 10.1007/s10878-015-9955-x
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    References listed on IDEAS

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    1. Shasha Li & Xueliang Li, 2012. "Note on the hardness of generalized connectivity," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 389-396, October.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.

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