2022/12/19 by Andrzej Grzesik, Grzesik, Andrzej, Daniel Il’kovič +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Decision Sciences · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Game Theory and Applications #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.2212.09343
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.