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\(Quasi _{\textrm{ps}}\)-Pancyclicity of Regular Multipartite Tournament

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Abstract

The study of arc-pancyclicity of tournaments has a long history. Let T be a regular c-partite tournament with partite sets \(V_1,V_2,\ldots ,V_c\). Alspach proved that every arc of a regular tournament is in a k-cycle for each \(k\in \{3,4,\ldots , n \}\). In this paper, we extend the concept of arc-pancyclicity of regular tournaments to regular multipartite tournaments. We prove that for any regular c-partite (\(c\ge 3\)) tournament T, if \([V_i,V_j]\ne \emptyset \), then there is a \((V_j, V_i)\)-path in T that transverses exactly k partite sets for each \(k\in \{4, \ldots , c\}\). This theorem is best possible in some sense and it confirms a conjecture proposed by Guo.

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Acknowledgements

We would like to thank all reviewers for their careful reading of the manuscript and detailed comments that significantly improved the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Weifang University, Weifang, 261061, China

    Jiansheng Cai

  2. Department of Mathematics, West Virginia University, Morgantown, WV, 26505, USA

    Weihao Xia

  3. Academy of Mathematics and System Science, Chinese Academy of Science, Beijing, 100190, China

    Guiying Yan

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  1. Jiansheng Cai
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  2. Weihao Xia
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  3. Guiying Yan
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Correspondence to Jiansheng Cai.

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This work is supported by NSFC (12071351, 11571258) and NSFSPD (ZR2020MA043).

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Cai, J., Xia, W. & Yan, G. \(Quasi _{\textrm{ps}}\)-Pancyclicity of Regular Multipartite Tournament. Graphs and Combinatorics 39, 91 (2023). https://doi.org/10.1007/s00373-023-02689-x

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  • DOI: https://doi.org/10.1007/s00373-023-02689-x

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