No additional tournaments are quasirandom-forcing

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Authors

HANCOCK Robert Arthur KABELA Adam KRÁĽ Daniel MARTINS Taisa PARENTE Roberto SKERMAN Fiona VOLEC Jan

Year of publication 2023
Type Article in Periodical
Magazine / Source European Journal of Combinatorics
MU Faculty or unit

Faculty of Informatics

Citation
Web http://doi.org/10.1016/j.ejc.2022.103632
Doi http://dx.doi.org/10.1016/j.ejc.2022.103632
Keywords tournaments; quasirandomness
Description A tournament H is quasirandom-forcing if the following holds for every sequence (Gn)n is an element of 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 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.(c) 2022 Published by Elsevier Ltd.
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