The join-ear equality does not extend beyond graphic matroids, but the two parameters stay within a factor of 6 for all regular matroids.
Frank.Connections in combinatorial optimization, volume 38 ofOxford Lecture Series in Mathematics and its Applications
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Joins and ear decompositions beyond graphic matroids
The join-ear equality does not extend beyond graphic matroids, but the two parameters stay within a factor of 6 for all regular matroids.