Huynh–Wood conjecture on subgraph counts in degenerate graphs

Let $d$ be a nonnegative integer, let $\mathcal D_d$ be the class of $d$-degenerate graphs, and let $H$ be a $d$-degenerate graph. For a graph $H$, let $\operatorname{flap}_d(H)$ denote the maximum size of an independent collection of separations of $H$ of order at most $d$. Huynh–Wood's conjecture.

$$\operatorname{ex}(H,\mathcal D_d,n)=\Theta\left(n^{\operatorname{flap}_d(H)}\right).$$

The paper identifies this as an equivalent form of a conjecture of Huynh and Wood. Its status is not resolved in the supplied text.