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arXiv · 1912.04243

No additional tournaments are quasirandom-forcing

Robert Hancock·Adam Kabela·Daniel Kral·Taisa Martins·Roberto Parente·Fiona Skerman·Jan Volec
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Abstract

A tournament H is quasirandom-forcing if the following holds for every sequence (G_n) of tournaments of growing orders: if the density of H in G_n converges to the expected density of H in a random tournament, then (G_n) is quasirandom. Every transitive tournament with at least 4 vertices is quasirandom-forcing, and Coregliano et al. [Electron. J. Combin. 26 (2019), P1.44] showed that there is also a non-transitive 5-vertex tournament with the property. We show that no additional tournament has this property. This extends the result of Bucic et al. [Combinatorica 41 (2021), 175-208] that the non-transitive tournaments with seven or more vertices do not have this property.

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Robert Hancock, Adam Kabela, Daniel Kral, Taisa Martins, Roberto Parente, Fiona Skerman, Jan Volec. 2019-12-09. No additional tournaments are quasirandom-forcing. https://doi.org/10.1016/j.ejc.2022.103632

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