2 problems

Detachable-pair classification conjecture. Either $M$ has a detachable pair; $M$ is a spike; $M \cong M(K_{3,k})$ or $M \cong M^*(K_{3,k})$ for some $k \ge 5$; $M$ is the cycle mat…

Independent set conjecture. If $M$ is a triangle-free $3$-connected matroid with a simple $3$-connected minor $N$, then $M$ has an independent set $I$ of $N$-contractible elements…