Quasirandom-Forcing Orientations of Cycles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F23%3A00132240" target="_blank" >RIV/00216224:14330/23:00132240 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/full/10.1137/23M1548700" target="_blank" >https://epubs.siam.org/doi/full/10.1137/23M1548700</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/23M1548700" target="_blank" >10.1137/23M1548700</a>

Result language
angličtina
Original language name
Quasirandom-Forcing Orientations of Cycles
Original language description
An oriented graph H is quasirandom-forcing if the limit (homomorphism) density of H in a sequence of tournaments is 2|H| if and only if the sequence is quasirandom. We study generalizations of the following result: the cyclic orientation of a cycle of length l is quasirandom-forcing if and only if l ≡ 2 mod 4. We show that no orientation of an odd cycle is quasirandom-forcing. In the case of even cycles, we find sufficient conditions on an orientation to be quasirandom-forcing, which we complement by identifying necessary conditions. Using our general results and spectral techniques used to obtain them, we classify which orientations of cycles of length up to 10 are quasirandom-forcing.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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