On the excluded minor structure theorem for graphs of large treewidth

Details On the excluded minor structure theorem for graphs of large treewidth On the excluded minor structure theorem for graphs of large treewidth

2009-10-06

arxiv.org/abs/0910.0946v2

Mathematics

Combinatorics

Scientific paper

At the core of the Robertson-Seymour theory of graph minors lies a powerful structure theorem which captures, for any fixed graph H, the common structural features of all the graphs not containing H as a minor. Robertson and Seymour prove several versions of this theorem, each stressing some particular aspects needed at a corresponding stage of the proof of the main result of their theory, the graph minor theorem. We prove a new version of this structure theorem: one that seeks to combine maximum applicability with a minimum of technical ado, and which might serve as a canonical version for future applications in the broader field of graph minor theory. Our proof departs from a simpler version proved explicitly by Robertson and Seymour. It then uses a combination of traditional methods and new techniques to derive some of the more subtle features of other versions as well as further useful properties, with substantially simplified proofs.

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