Graph minors. XVIII. tree-decompositions and well-quasi-ordering

Authors:
Neil Robertson;Paul Seymour
Affiliations:
Math Department, Ohio State University, 231 W 18th Ave, Columbus, OH;Telcordia Technologies, 445 South St., Morristown, NJ and Princeton University, Princeton, NJ
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

Citing 2
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Abstract

We prove the following result. Suppose that for every graph G in a class C of graphs, and for every "highly connected component" of G, there is a decomposition of G of a certain kind centred on the component. Then C is well-quasi-ordered by minors; that is, in any infinite subset of C there are two graphs, one a minor of the other. This is another step towards Wagner's conjecture.