Precise determination of universal obstructions for specific classes H

Determine explicitly the finite set 2min of universal obstructions for H-treewidth for particular minor-closed classes H by fully characterizing the parametric graphs that survive the minimization, beyond the surface-based families already handled.

Background

While the paper provides general constructions of universal obstructions, the exact identification of the minimal obstruction families 2min for specific minor-closed classes H remains unresolved.

They note initial progress for certain surface-based families in a companion work [56], but emphasize that a general, precise determination across further classes remains open.