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

On the excluded minor structure theorem for graphs of large treewidth