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Edge-Disjoint Steiner Trees and Connectors in Graphs

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Abstract

Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If \(S\subseteq V(G)\) is 2k-edge-connected in a graph G,  then G contains k edge-disjoint S-Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If \(S\subseteq V(G)\) is 3k-edge-connected in a graph G,  then G contains k edge-disjoint S-connectors, which is an analogue for S-connectors of Kriesell’s Conjecture. This paper shows If \(|V(G) - S| \le k,\) then Conjecture 1 is true and if \(|V(G) - S| \le 2k,\) then Conjecture 2 is true. This paper also investigate the validity of two conjectures with certain additional conditions of \(|V(G) - S|\) or |S|.

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Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by Henan Educational Committee [22A110003], the Foundation of Department of Science and Technology of Henan [HNGD2022060] and the Foundation of Henan Normal University [20200146].

Funding

This work was supported by Henan Educational Committee [22A110003], the Foundation of Department of Science and Technology of Henan [HNGD2022060] and the Foundation of Henan Normal University [20200146].

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, ** Mao

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  1. Hengzhe Li
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  2. Huayue Liu
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  3. Jianbing Liu
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  4. Ya** Mao
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Contributions

All authors contributed to the study conception and design. All authors commented on previous versions of the manuscript and all authors read and approved the final manuscript. Hengzhe Li: methodology, funding acquisition, writing-original draft. Huayue Liu: methodology, validation. Jianbing Liu: validation, writing, supervision-review and editing. Ya** Mao: conceptualization, validation, investigation.

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Correspondence to Jianbing Liu.

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Li, H., Liu, H., Liu, J. et al. Edge-Disjoint Steiner Trees and Connectors in Graphs. Graphs and Combinatorics 39, 23 (2023). https://doi.org/10.1007/s00373-023-02621-3

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  • DOI: https://doi.org/10.1007/s00373-023-02621-3

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