Degenerate-graph density conjecture

For $k\in\mathbb{N}_0$, let $\mathcal{D}_k$ be the class of $k$-degenerate graphs. Let $f_k(H)$ be the separation parameter defined by taking $f_k(H)=1$ when $H$ has no $(\leqslant k)$-separation, and otherwise taking the maximum number of pairwise independent $(\leqslant k)$-separations in $H$.

Degenerate-graph density conjecture. For every fixed $k$-degenerate graph $H$,

$$C(H,\mathcal{D}_k,n) \in \Theta\left(n^{f_k(H)}\right).$$

This is proposed as a generalisation of the paper's bounds for degenerate graph classes. The source does not report a proof or disproof, so the conjecture remains open.