Quasirandom-Forcing Orientations of Cycles
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | SIAM JOURNAL ON DISCRETE MATHEMATICS |
| MU Faculty or unit | |
| Citation | |
| Web | https://epubs.siam.org/doi/full/10.1137/23M1548700 |
| Doi | http://dx.doi.org/10.1137/23M1548700 |
| Keywords | quasirandomness; tournaments; cycles; quasirandom graphs; combinatorial limits |
| 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. |
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