Existence of infinitely many non-transitive forcing tournaments

Determine whether infinitely many non-transitive tournaments force quasirandomness in regular tournaments.

Background

The paper observes that a classification of tournaments forcing quasirandomness in regular tournaments might reveal only finitely many non-transitive examples, as happens for tournaments without the regularity assumption.

The authors identify the existence of an infinite family of non-transitive forcing tournaments as a first step toward the broader classification problem.