Lina Simbaqueba Marin
- BSc (Universidad Nacional de Colombia, 2023)
Topic
Quasirandom forcing in Regular Tournaments
Department of Mathematics and Statistics
Date & location
- Friday, April 11, 2025
- 10:00 A.M.
- Clearihue Building, Room B021
Examining Committee
Supervisory Committee
- Dr. Jonathan Noel, Department of Mathematics and Statistics, University of Victoria (Supervisor)
- Dr. Jane Butterfield, Department of Mathematics and Statistics, UVic (Co-Supervisor)
External Examiner
- Dr. Leonardo Coregliano, Department of Mathematics, University of Chicago
Chair of Oral Examination
- Dr. Clifford Roberts, Department of Philosophy, UVic
Abstract
The study of quasirandom forcing in various discrete structures has been a wellk-nown problem in Extremal Combinatorics since 1987. In this work, we study quasirandom forcing in the case of tournaments. A tournament 𝐻 forces quasirandomness if it has the property that every sequence (𝑇𝑛)𝑛∈ℕ of tournaments of increasing order is quasirandom if and only if the density of 𝐻 in 𝑇𝑛 asymptotically equals its expected value as 𝑛→∞. In contrast to the analogous problem in graphs, it was shown that there exists only one non-transitive tournament that forces quasirandomness. To obtain a richer family of tournaments with this property, we propose a variant of it restricting the definition of quasirandom forcing to only nearly regular sequences of tournaments (𝑇𝑛)𝑛∈ℕ. We characterize all tournaments on at most 5 vertices that forces quasirandomness under this new setting, obtaining that 11 out of 16 tournaments on at least four vertices are quasirandom forcing.