Polynomial bound on the size of universal obstructions

Improve the current double-exponential bound on the number of universal obstructions (e.g., the cardinalities of obstructing sets such as 2H or 3H) to a bound that is polynomial in h, where h is the maximum size of an obstruction of H.

Background

The paper currently derives double-exponential bounds (in terms of h) on the sizes of their universal obstruction families, which impacts the practicality of constructing embedding pairs and parametric graphs.

They conjecture that much smaller bounds should be achievable, ideally polynomial in h, though they note this may require accepting worse gap functions.