TOWARDS A MATROID-MINOR STRUCTURE THEORY
Jim Geelen, Bert Gerards, Geoff Whittle · Oxford University Press eBooks · 2007
This chapter surveys recent work aimed at generalizing the results and techniques of the Graph Minors Project of Robertson and Seymour to matroids. Some of the most interesting and apparently difficult conjectures in matroid theory concern minor-closed classes. Three fundamental conjectures of this type are described, the most famous of which is perhaps Rota's Conjecture. A minor-minimal matroid that does not belong to a given minor-closed class of matroids is an excluded minor for that class.