No additional tournaments are quasirandom-forcing

12/09/2019

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by   Robert Hancock, et al.

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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.