No additional tournaments are quasirandom-forcing

No additional tournaments are quasirandom-forcing

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 quasira...

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Bibliographic Details
Main Authors: Hancock, Robert, Kabela, Adam, Kral, Daniel, Martins, Taisa, Parente, Roberto, Skerman, Fiona, Volec, Jan
Format: Journal Article
Language:English
Published: 20-09-2022
Subjects:
Computer Science - Discrete Mathematics
Mathematics - Combinatorics
Online Access:Get full text
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Summary: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. This extends the result of Bucic et al. [Combinatorica 41 (2021), 175-208] that the non-transitive tournaments with seven or more vertices do not have this property.
DOI:10.48550/arxiv.1912.04243