Publication details
Cycles of length three and four in tournaments
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Combinatorial Theory, Series A |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1016/j.jcta.2020.105276 |
| Doi | http://dx.doi.org/10.1016/j.jcta.2020.105276 |
| Keywords | Tournaments; Cycles; Extremal combinatorics |
| Description | 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. |