### Abstract

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. [arXiv:1910.09936] that the non-transitive tournaments with seven or more vertices do not have this property.

Original language | English |
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Number of pages | 14 |

Publication status | Submitted - 2019 |

### Publication series

Name | arXiv |
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Publisher | Cornell University |

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## Cite this

Skerman, F., Hancock, R., Kabela, A., Kral, D., Martins, T., Parente, R., & Volec, J. (2019).

*No additional tournaments are quasirandom forcing*. (arXiv). https://arxiv.org/abs/1912.04243