3 problems

Let $M_1$ be a matroid with a circuit-hyperplane $H$, and let $M_2$ be obtained from $M_1$ by relaxing $H$. If both $M_1$ and $M_2$ are representable over a finite field…

Matroid structure theorem. The stated tree-decomposition exists.

Let $N$ be a $\operatorname{GF}(q)$-representable matroid, and let $\operatorname{bw}(M)$ denote the branch width of a matroid $M$. High-branch-width non-fragility conjecture. Ther…