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A solution to a conjecture on the generalized connectivity of graphs

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Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

The generalized k-connectivity \(\kappa _k(G)\) 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.

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Acknowledgments

Supported by NSFC (Nos. 11071130, 11161037, 11501223, 11501271), the “973” program, the Scientific Research Funds of Huaqiao University (No. 14BS311), and the Science Found of Qinghai Province (No. 2014-ZJ-907).

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Authors and Affiliations

  1. School of Mathematics Science, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Lily Chen

  2. Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin, 300071, People’s Republic of China

    Lily Chen, Xueliang Li, Mengmeng Liu & Yaping Mao

  3. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, 730070, People’s Republic of China

    Mengmeng Liu

  4. Department of Mathematics, Qinghai Normal University, Xining, 810008, Qinghai, People’s Republic of China

    Yaping Mao

Authors
  1. Lily Chen
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  2. Xueliang Li
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  3. Mengmeng Liu
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  4. Yaping Mao
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Correspondence to Lily Chen.

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Chen, L., Li, X., Liu, M. et al. A solution to a conjecture on the generalized connectivity of graphs. J Comb Optim 33, 275–282 (2017). https://doi.org/10.1007/s10878-015-9955-x

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  • DOI: https://doi.org/10.1007/s10878-015-9955-x

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