| GRZESIK, Andrzej, Daniel IĽKOVIČ, Bartłomiej KIELAK a Daniel KRÁĽ. Quasirandom-Forcing Orientations of Cycles. SIAM JOURNAL ON DISCRETE MATHEMATICS. UNITED STATES: SIAM PUBLICATIONS, 2023, roč. 37, č. 4, s. 2689-2716. ISSN 0895-4801. Dostupné z: https://dx.doi.org/10.1137/23M1548700. |
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@article{2339297,
author = {Grzesik, Andrzej and Iľkovič, Daniel and Kielak, Bartłomiej and Kráľ, Daniel},
article_location = {UNITED STATES},
article_number = {4},
doi = {http://dx.doi.org/10.1137/23M1548700},
keywords = {quasirandomness; tournaments; cycles; quasirandom graphs; combinatorial limits},
language = {eng},
issn = {0895-4801},
journal = {SIAM JOURNAL ON DISCRETE MATHEMATICS},
title = {Quasirandom-Forcing Orientations of Cycles},
url = {https://epubs.siam.org/doi/full/10.1137/23M1548700},
volume = {37},
year = {2023}
}
TY - JOUR
ID - 2339297
AU - Grzesik, Andrzej - Iľkovič, Daniel - Kielak, Bartłomiej - Kráľ, Daniel
PY - 2023
TI - Quasirandom-Forcing Orientations of Cycles
JF - SIAM JOURNAL ON DISCRETE MATHEMATICS
VL - 37
IS - 4
SP - 2689-2716
EP - 2689-2716
PB - SIAM PUBLICATIONS
SN - 08954801
KW - quasirandomness
KW - tournaments
KW - cycles
KW - quasirandom graphs
KW - combinatorial limits
UR - https://epubs.siam.org/doi/full/10.1137/23M1548700
N2 - 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.
ER -
GRZESIK, Andrzej, Daniel IĽKOVIČ, Bartłomiej KIELAK a Daniel KRÁĽ. Quasirandom-Forcing Orientations of Cycles. \textit{SIAM JOURNAL ON DISCRETE MATHEMATICS}. UNITED STATES: SIAM PUBLICATIONS, 2023, roč.~37, č.~4, s.~2689-2716. ISSN~0895-4801. Dostupné z: https://dx.doi.org/10.1137/23M1548700.
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