2 problems

Structural conjecture. The class of $3$-connected binary matroids that do not contain $M(K_4)$ as an induced minor is exactly the class of matroids that can be obtained by starting…

Partial lift-join structure conjecture. For all $s,t\geq 1$ there exists $k\geq 2$ such that, if $M$ is a matroid with $\omega(M)\leq s$ and $\sigma(M)\leq t$, then $M$ can be cons…