Open Problems related to computing obstruction sets

Robertson and Seymour proved Wagner’s famous Conjecture and showed that every minor ideal has a polynomial time decision algorithm. The algorithm uses the obstructions of the minor ideal. By Robertson and Seymour’s proof we know that there are only finitely many such obstructions. Nevertheless, the proof is non-constructive and for many minor ideals we do not know the obstructions. Since the 1980ies, research has been done to overcome this non-constructiveness, but many interesting problems still remain unsolved. This is a small collection of open problems in the field of computing obstructions for minor ideals. We give a short introduction to the open problems from a paper by Adler, Grohe and Kreutzer [2], and to other open problems. This collection is meant to stimulate research in this area and it is far from exhaustive.

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[16]  Stephan Kreutzer,et al.  Computing excluded minors , 2008, SODA '08.

[17]  Martin Grohe.  Local Tree-Width, Excluded Minors, and Approximation Algorithms , 2003, Comb..