$\newcommand{\N}{\mathbb{N}}\newcommand{\Z}{\mathbb{Z}}\newcommand{\R}{\mathbb{R}}\DeclareMathOperator{\E}{E}$

A graph class $\mathcal{G}$ is monotone if, for every $G\in\mathcal{G}$, every subgraph of $G$ is also in $\mathcal{G}$. A graph class $\mathcal{G}$ is small if the number of $n$-vertex graphs in $\mathcal{G}$ is $2^{\Theta(n)}n!$. Lots of interesting graph classes are small.

Édouard Bonnet, Julien Duron, John Sylvester, Viktor Zamaraev, Maksim Zhukovskii show that every graph in a small monotone graph class is $d$-degenerate for some $d$ that depends on the constant in the $\Theta$ notation.

Problem: Find some interesting applications of this result