Cycles of length three and four in tournaments

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00118501" target="_blank" >RIV/00216224:14330/20:00118501 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jcta.2020.105276" target="_blank" >http://dx.doi.org/10.1016/j.jcta.2020.105276</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jcta.2020.105276" target="_blank" >10.1016/j.jcta.2020.105276</a>

Result language
angličtina
Original language name
Cycles of length three and four in tournaments
Original language 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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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