Detecting Matroid Minors

When % is a collection of matroids, the question whether M has a minor in % can be easy or hard, depending on the choice of < 6. More precisely, the number of demands made on an "independence oracle" to decide the question sometimes can be bounded above by a polynomial in \E(M)\, and sometimes it cannot. We study this, and in particular classify each singleton % as easy or hard.

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