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\(Z_3\)-Connectivity with Independent Number 2

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Abstract

Let \(G\) be a 3-edge-connected graph on \(n\) vertices. It is proved in this paper that if \(\alpha (G)\le 2\), then either \(G\) can be \(Z_3\)-contracted to one of graphs \(\{K_1, K_4\}\) or \(G\) is one of the graphs in Fig. 1.

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Authors and Affiliations

  1. School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, 212003, Jiangsu, China

    Fan Yang

  2. Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China

    Xiangwen Li

  3. School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471022, China

    Liangchen Li

Authors
  1. Fan Yang
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  2. Xiangwen Li
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  3. Liangchen Li
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Corresponding author

Correspondence to Fan Yang.

Additional information

F. Yang Research is partially supported by NSF-China Grant: NSFC 11326215 and NSFC 11371009. Research is partially supported by Natural Science Foundation of Jiangsu Province of China: BK20130472. X. Li Research is partially supported by NSF-China Grant: NSFC: 11171129 and by Doctoral Fund of Ministry of Education of China (20130144110001). L. Li Research is partially supported by NSF-China Grant: NSFC: 11301254.

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Yang, F., Li, X. & Li, L. \(Z_3\)-Connectivity with Independent Number 2 . Graphs and Combinatorics 32, 419–429 (2016). https://doi.org/10.1007/s00373-015-1556-z

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  • DOI: https://doi.org/10.1007/s00373-015-1556-z

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