The cograph formulation of the Erdős–Hajnal conjecture

Let $H$ be a graph. A cograph is either a single-vertex graph or a graph obtained by taking the vertex-disjoint union of two smaller cographs whose vertex sets form a pure pair. A graph $G$ is $H$-free if it has no induced subgraph isomorphic to $H$.

Cograph formulation of the Erdős–Hajnal conjecture. For every graph $H$, there exists an $\varepsilon>0$ such that every $n$-vertex $H$-free graph $G$ contains an induced cograph of order $n^{\varepsilon}$.

Because cographs are perfect, this formulation is equivalent to the original Erdős–Hajnal conjecture. It is presented as a convenient reformulation for the paper's proof, while the conjecture remains open.