Title: Computing excluded minors

Robertson and Seymour's proof of Wagner's conjecture implies
that every minor closed class of graphs can be characterised 
by a finite set of excluded minors, a finite so-called "obstruction set".

The theorem is highly non-constructive. For example, the class of all 
knot free graphs is closed under minors and hence it can be characterised 
by a finite obstruction set. But we do not know such an obstruction set.

While in general such finite obstruction sets may not be computable, 
we show that for some classes they are, such as unions of minor closed 
classes, and for every k the class of graphs of tree-width at most k.

This is joint work with Martin Grohe and Stephan Kreutzer.