No additional tournaments are quasirandom-forcing - Hancock, Robert; Kabela, Adam; Král’, Daniel; Martins, Taísa; Parente, Roberto; Skerman, Fiona; Volec, Jan (European journal of combinatorics, 2023)
A tournament H is quasirandom-forcing if the following holds for every sequence (Gn)n∈N of tournaments of growing orders: if the density of H in Gn converges to the expected density of H in a random tournament, then (Gn)n∈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 Bucić (2021) that the non-transitive tournaments with seven or more vertices do not have this property.