For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state a num- ber of conjectures that might be approachable using the structural characterization.
Additional Metadata
Keywords matroids, minors, connectivity, girth, linear codes, ML threshold function, growth rate
MSC Matroids, geometric lattices (msc 05B35)
THEME Other (theme 6)
Publisher Birkhäuser
Persistent URL
Journal Annals of Combinatorics
Geelen, J, Gerards, A.M.H, & Whittle, G. (2015). The Highly Connected Matroids in Minor-closed Classes. Annals of Combinatorics, 19(1), 107–123. doi:10.1007/s00026-015-0251-3