 
Summary: Open Problems related to computing
obstruction sets
Isolde Adler
Humboldt University Berlin, Germany
adler@informatik.huberlin.de
13th September 2008
Abstract
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 nonconstructive and for many minor ideals we
do not know the obstructions. Since the 1980ies, research has been done to overcome this
nonconstructiveness, 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.
1 Introduction
Graphs are finite and simple. For a graph G we denote the vertex set by V (G) and the edge set by
E(G). Let G be a graph and {u, v} E(G). By contracting the edge {u, v} we mean the following
