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

  • Shipeng Wang
  • Shoichi Tsuchiya
  • Liming Xiong
Original Paper


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 RS such that every connected \(\{R,S\}\)-free graph has the same (vertex)-connectivity and edge-connectivity.


Connectivity Edge connectivity Forbidden subgraph 



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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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingPeople’s Republic of China
  2. 2.School of Network and InformationSenshu UniversityKawasakiJapan
  3. 3.School of Mathematics and Statistics, Beijing Key Laboratory on MCAACIBeijing Institute of TechnologyBeijingPeople’s Republic of China

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