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Forbidden Pairs for Equality of Connectivity and Edge-Connectivity of Graphs

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Abstract

Let \({\mathcal {H}}\) be a set of connected graphs. A graph is said to be \({\mathcal {H}}\)-free if it does not contain any member of \({\mathcal {H}}\) as an induced subgraph. In this paper, we characterize all pairs R, S such that every connected \(\{R,S\}\)-free graph has the same (vertex)-connectivity and edge-connectivity.

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Acknowledgements

The first author is funded by International Graduate Exchange Program of Beijing Institute of Technology. The second author is partially supported by JSPS KAKENHI Grant number JP16K17646. The third author is supported by the Natural Science Funds of China (Nos: 11871099, 11671037).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Shipeng Wang

  2. School of Network and Information, Senshu University, 2-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa, 214-8580, Japan

    Shoichi Tsuchiya

  3. School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Liming Xiong

Authors
  1. Shipeng Wang
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  2. Shoichi Tsuchiya
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  3. Liming Xiong
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Correspondence to Liming Xiong.

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Wang, S., Tsuchiya, S. & Xiong, L. Forbidden Pairs for Equality of Connectivity and Edge-Connectivity of Graphs. Graphs and Combinatorics 35, 419–426 (2019). https://doi.org/10.1007/s00373-018-2003-8

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  • DOI: https://doi.org/10.1007/s00373-018-2003-8

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