CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F19%3A00113681" target="_blank" >RIV/00216224:14330/19:00113681 - isvavai.cz</a>
Result on the web
<a href="http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222" target="_blank" >http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222</a>
DOI - Digital Object Identifier
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Alternative languages
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Mathematica Universitatis Comenianae
ISSN
0231-6986
e-ISSN
0862-9544
Volume of the periodical
88
Issue of the periodical within the volume
3
Country of publishing house
SK - SLOVAKIA
Number of pages
7
Pages from-to
533-539
UT code for WoS article
000484349000029
EID of the result in the Scopus database
2-s2.0-85073776596