Existence of extremal graphs for every degeneracy

Let $d$ be an integer with $d\geq 2$. A graph is $d$-degenerate if every subgraph has a vertex of degree at most $d$. Let $f(H,p)$ denote the subgraph query complexity, and write $b$ for the relevant query parameter.

Extremal graph existence conjecture. For every integer $d\geq 2$, there exists a $d$-degenerate graph $H$ such that

$$f(H,p)=b^{d-o(1)}.$$

In the case $d=2$, the paper constructs such a graph, whereas the existence of such graphs for $d\geq 3$ remains open.