2 problems

Jackson–Tanigawa's hyperconnectivity conjecture. For $d\geq 1$ and $\mathcal{X}=\{K_{d+2},K_{d+1,d+1}\}$, $\mathcal{H}_n^d$ is the unique maximal $\mathcal{X}$-matroid, and…

Kalai–Whiteley maximality conjecture. The matroid $\mathcal{H}_d(n)$ is the freest matroid in which every $K_{d+2}$ and every $K_{d+1,d+1}$ are circuits.