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arXiv · 2602.12551

Sidorenko property and forcing in regular tournaments

Daniel Král'·Matjaž Krnc·Filip Kučerák·Bernard Lidický·Jan Volec
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Abstract

We give a complete characterization of tournaments H that have the Sidorenko property with respect to nearly regular tournaments, i.e., the homomorphism density of H among all nearly regular tournaments is minimized by a random tournament. Corollaries of our result are a positive answer to the question of Noel, Ranganathan and Simbaqueba whether there exist infinitely many non-transitive tournaments that are quasirandom forcing for nearly regular tournaments, and a negative answer to their question whether almost every tournament is quasirandom forcing for nearly regular tournaments.

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Daniel Král', Matjaž Krnc, Filip Kučerák, Bernard Lidický, Jan Volec. 2026-02-13. Sidorenko property and forcing in regular tournaments. https://arxiv.org/abs/2602.12551

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