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.
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Networks and Optimization

Hall, R., Mayhew, D., & van Zwam, S. (2011). On the relative importance of excluded minors. arXiv.org e-Print archive. Cornell University Library .