6 Conclusion
Any graphic matroid is good. Any cographic matroid is good. Any matroid isomorphic to R10 is good. Any 1-sum (in the sense of Definition 36) of good matroids is a good matroid. Any 2-sum (in the sense of Definition 41) of good matroids is a good matroid. Any 3-sum (in the sense of Definition 47) of good matroids is a good matroid.
Any good matroid is regular. This is a corollary of the easy direction of the Seymour theorem.
Proof
Structural induction.