Sidorenko property and quasirandomness in regular tournaments

We give a complete characterization of tournaments \(H\) that have the Sidorenko property with respect to nearly regular tournaments, i.e., the density of \(H\) among all nearly regular tournaments is minimized by a random tournament. Our result answers two questions of Noel, Ranganathan and Simbaqueba regarding quasirandom forcing in the setting of nearly regular tournaments.

This is a joint work with Dan Kráľ, Matjaž Krnc, Filip Kučerák and Bernard Lidický.