In  it was shown that if M is a 3-connected matroid with a minor isomorphic to U24, then every pair of elements of M are in a U24 minor. The proof was fairly complicated. Here we derive that theorem from a more general result. We show that to test whether U24 (or any other 3-connected matroid N) has the property described above, it is only necessary to test that it works for those matroids M with 5 (or more generally, |E (N)| + 1) elements. This is essentially a lemma which will be used in a subsequent paper.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics