Data: 21/05/2020, às 14:00 horas (GMT-3, horário de Brasília).
Título: Quasirandom-forcing tournaments
Palestrante: Taísa Martins (UFF)


Abstract: A tournament H is quasirandom-forcing if the following holds for every sequence (G_n)_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)_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.

This is joint work with Robert Hancock, Adam Kabela, Dan Král', Roberto Parente, Fiona Skerman and Jan Volec.