Joins and ear decompositions beyond graphic matroids

Yuhang Bai, Kristóf Bérczi, Chaitanya Nalam

For a matroid $M$, a join is a set $J\subseteq E(M)$ that meets every circuit $C$ in at most $|C|/2$ elements. Let $\mu (M)$ denote the maximum size of a join. Motivated by Frank's mi…