If EE is a set of matroids, then ex(EE) denotes the set of matroids that have no minor isomorphic to a member of EE. If EE' is a subset of EE, we say that EE' is /superfluous/ if ex(EE - EE') - ex(EE) contains only finitely many 3-connected matroids. We characterize the superfluous subsets of six well-known collections of excluded minors.
, , ,
Advances in Applied Mathematics
Matroid Structure for Efficiency
Networks and Optimization

Hall, R., Mayhew, D., & van Zwam, S. (2011). On the relative importance of excluded minors. Advances in Applied Mathematics, 50(1), 228–242. doi:10.1016/j.aam.2012.08.007