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The Asymmetry Number of Finite Tournaments, and Some Related Results

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Abstract

We introduce the concept of asymmetry number for finite tournaments, as a natural generalization of that for graphs by Erdős and Rényi (Acta Math Acad Sci Hungar 14:295–315, 1963). We prove an upper bound for the asymmetry number of finite tournaments and discuss its asymptotically best possibility. We also give an alternative proof of a theorem by Jaligot and Khelif (Aequat Math 67:73–79, 2004) which states that the random tournament can be expressed by a Cayley tournament on an arbitrary countable group without involutions. We slightly improve a result by Cameron and Johnson (Math Proc Camb Philos Soc 102:223–231, 1987).

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Acknowledgements

The author would like to thank Masanori Sawa for his careful reading of this paper and many valuable comments and suggestions.

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  1. Graduate School of Information Science, Nagoya University Furo, Chikusa, Nagoya, 464-8601, Japan

    Shohei Satake

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  1. Shohei Satake
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Correspondence to Shohei Satake.

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Satake, S. The Asymmetry Number of Finite Tournaments, and Some Related Results. Graphs and Combinatorics 33, 1433–1442 (2017). https://doi.org/10.1007/s00373-017-1787-2

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