On the relative importance of excluded minors

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

On the relative importance of excluded minors

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

On the relative importance of excluded minors

If E is a set of matroids, then EX(E) denotes the set of matroids that have no minor isomorphic to a member of E. If E′ E, we say that E′ is superfluous if EX(E-E′)-EX(E) contains only finitely many 3-connected matroids. We determine the superfluous subsets of six well-known collections of excluded minors. © 2012 Elsevier Inc