Upper bounds on the size of obstructions and intertwines (Q1272647)

An upper bound is given in \(p^4\) on the size of any obstruction for path-width at most \(p\), and a doubly exponential upper bound in \(k^5\) on the size of any obstruction for tree-width at most \(k\). Further results are given that lead on to a constructive proof that, if a minor closed family \(L\) has finite \(p\)-length and has obstruction of path-width at most \(p\), then \(L\) has a finite number of obstructions. Further upper bounds are also obtained.