HANCOCK, R., et al. No additional tournaments are quasirandom-forcing. European Journal of Combinatorics. 2023, 108 ISSN 0195-6698. DOI 10.1016/j.ejc.2022.103632.
A tournament H is quasirandom-forcing if the following holds for every sequence (G_n) is an element of 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 an element of N is quasirandom. Every transitive tournament with at least 4 vertices is quasirandom-forcing, and Coregliano (2019) 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 (2021) that the non-transitive tournaments with seven or more vertices do not have this property.
