Quasirandom forcing in regular tournaments
| dc.contributor.author | Simbaqueba Marin, Lina | |
| dc.contributor.supervisor | Noel, Jonathan | |
| dc.date.accessioned | 2025-05-01T22:05:58Z | |
| dc.date.available | 2025-05-01T22:05:58Z | |
| dc.date.issued | 2025 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science MSc | |
| dc.description.abstract | The study of quasirandom forcing in various discrete structures has been a well-known problem in Extremal Combinatorics since 1987. In this work, we study quasirandom forcing in the case of tournaments. We say that a tournament H forces quasirandomness if in every quasirandom sequence (T_n)_{n\in \mathbb{N}} of tournaments of increasing order, the density of H in T_n asymptotically equals its expected value. 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 (T_n)_{n\in \mathbb{N}}. We characterize all tournaments on at most 5 vertices that force quasirandomness under this new setting, obtaining that 11 out of 16 tournaments on four or five vertices are quasirandom forcing in sequences of nearly regular tournaments. | |
| dc.description.scholarlevel | Graduate | |
| dc.identifier.uri | https://hdl.handle.net/1828/22091 | |
| dc.language | English | eng |
| dc.language.iso | en | |
| dc.rights | Available to the World Wide Web | |
| dc.subject | Quasirandomness | |
| dc.subject | Extremal Combinatorics | |
| dc.subject | Tournaments | |
| dc.title | Quasirandom forcing in regular tournaments | |
| dc.type | Thesis |