Erdős–Hajnal polynomial Ramsey-number conjecture for hereditary classes

Let $X$ be a proper hereditary class of graphs, meaning that $X$ is not the class of all graphs. For natural numbers $p$ and $q$, let $R_X(p,q)$ be the least integer $n$ such that every graph in $X$ with at least $n$ vertices has either a clique of size $p$ or an independent set of size $q$.

Erdős–Hajnal conjecture. There are constants $A$ and $k$ such that

$$R_X(p,q)\leq A(p+q)^k$$

for every $p,q\in\mathbb{N}$; equivalently, Ramsey numbers grow at most polynomially in $X$.

This is the paper’s formulation of the Erdős–Hajnal conjecture. The supplied text gives no resolution status.