The positive EH-coefficient conjecture for tournaments

A tournament is a directed graph with exactly one directed edge between each pair of distinct vertices. For a tournament $S$, a nonnegative real number $\epsilon$ is an EH-coefficient if there exists $c>0$ such that every $S$-free tournament $T$ satisfies $\alpha(T)\geq c|V(T)|^\epsilon$, where $\alpha(T)$ is the maximum size of a transitive subtournament.

Positive EH-coefficient conjecture. Every tournament has a positive EH-coefficient.

The source states that this is equivalent to the Erdős–Hajnal conjecture. Introducing the constant $c$ removes effects from tournaments of bounded order; the conjecture remains open in general.