Sidorenko property and forcing in regular tournaments
arXiv:2602.12551
The paper fully characterizes which tournaments have the Sidorenko property for nearly regular tournaments, showing that a random tournament minimizes homomorphism density, and resolves open questions about quasirandom forcing in this setting.
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.