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.
Online verfügbar 24 October 2022
Gesehen am 15.02.2023
The first, third and seventh authors were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 648509). The second, third and sixth authors were supported by the MUNI Award in Science and Humanities of the Grant Agency of Masaryk University. The fourth author was supported by CAPES, Brazil. This publication reflects only its authors’ view; the European Research Council Executive Agency is not responsible for any use that may be made of the information it contains