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On Cycles Containing a Given Arc in Regular Multipartite Tournaments

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Abstract

In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . ,n. Our result, in a sense, generalizes a theorem due to Alspach.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China

    Lin Qiang Pan

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

    Ke Min Zhang

Authors
  1. Lin Qiang Pan
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  2. Ke Min Zhang
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Corresponding author

Correspondence to Lin Qiang Pan.

Additional information

The project is supported by Chinese Postdoctoral Science Foundation, National Natural Science Foundation of China (Grant Nos. 60103021, 10171062 and 19871040), and Huazhong University of Science and Technology Foundation

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Pan, L.Q., Zhang, K.M. On Cycles Containing a Given Arc in Regular Multipartite Tournaments. Acta Math Sinica 20, 379–384 (2004). https://doi.org/10.1007/s10114-004-0327-1

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  • DOI: https://doi.org/10.1007/s10114-004-0327-1

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