Unfortunately, the result of Robertson and Seymour is non constructive in the sense that it does not provide any method of constructing the corresponding obstruction set. It is easy to check that the class of graphs with carving width bounded by k is immersion closed for any k. However, as in the case of cutwidth, an optimal constructive algorithm was missing. N. Robertson and P. D. Seymour. The disjoint paths problem .
G is a graph that is obtained from a subgraph of G by contracting edges.
N. Robertson and P.D. Seymour. The disjoint paths problem . Neil Robertson and Paul D. Seymour. N. Robertson, P. D. Seymour, Graph minors. The disjoint paths problem , preprint, revision of February 1992.