Finite-obstruction meta-conjecture for packing sparse graphs

Let $\mathcal{G}$ be any family of sparse graphs, and let $H$ be a dense graph on $n$ vertices. A simple obstruction is an evident necessary condition preventing a packing of $\mathcal{G}$ into $H$.

Finite-obstruction meta-conjecture. If there is no simple obstruction to packing $\mathcal{G}$ into $H$, then a packing exists; equivalently, there is a finite list of obstructions that characterizes when such a packing is possible.

The source presents this as a broad direction suggested by existing packing conjectures, while emphasizing that more subtle obstructions can occur, including parity and high-degree obstructions. It is not stated with a precise definition of “sparse,” “dense,” or “simple obstruction,” so the formulation remains informal and open.