Informace o publikaci
Cycles of length three and four in tournaments
| Autoři | |
|---|---|
| Rok publikování | 2020 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal of Combinatorial Theory, Series A |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | http://dx.doi.org/10.1016/j.jcta.2020.105276 |
| Doi | http://dx.doi.org/10.1016/j.jcta.2020.105276 |
| Klíčová slova | Tournaments; Cycles; Extremal combinatorics |
| Popis | Linial and Morgenstern conjectured that, among all n-vertex tournaments with d((n)(3)) cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for d >= 1/36 by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate that the family of extremal examples is broader than expected and give its full description for d >= 1/16. (C) 2020 Elsevier Inc. All rights reserved. |