Finite-obstruction meta-conjecture for packing sparse graphs

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

Finite-obstruction meta-conjecture. If there is no simple obstruction to packing G\mathcal{G} into HH, 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.

References

Primary source

Peter Allen, Julia Böttcher, Jan Hladký and Diana Piguet, “Packing degenerate graphs”, arXiv:1711.04869 (2022).

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