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On Explicit Random-Like Tournaments

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Abstract

We give a new theorem describing a relation between the quasi-random property of regular tournaments and their spectra. This provides many solutions to a constructing problem mentioned by Erdős and Moon (Can Math Bull 8(3):269–271, 1965) and Spencer (Graphs Comb 1(4):357–382, 1985).

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Acknowledgements

We are grateful to the editor and anonymous reviewers for their many helpful suggestions for improving the presentation. We would like to thank Masanori Sawa and Yujie Gu for their valuable comments. We also greatly appreciate Sergey Savchenko for his helpful remarks.

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  1. Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1, Kurokami, Chuo, Kumamoto, 860-8555, Japan

    Shohei Satake

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  1. Shohei Satake
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Correspondence to Shohei Satake.

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The author is supported by Grant-in-Aid for JSPS Fellows 18J11282 and 20J00469 of the Japan Society for the Promotion of Science.

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Satake, S. On Explicit Random-Like Tournaments. Graphs and Combinatorics 37, 1451–1463 (2021). https://doi.org/10.1007/s00373-021-02330-9

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