Random Tournaments Are Asymptotically Almost Surely Link-irregular

Source abstract

Bastien and Khormali (2025) conjectured that a nontrivial link-irregular tournament with $n$ vertices exists if and only if $n \ge 6$. Their work establishes the conjecture for $n \le 100$. We present a probabilistic argument for the existence of link-irregular tournaments with $n$ vertices when $n \ge 9$ to resolve the conjecture. In fact, we show that a random tournament is asymptotically almost surely link-irregular.