2 problems

Chepoi–Estellon–Vaxès conjecture. There exists a constant $c$ such that for every integer $r\geqslant 0$, every planar graph $G$, and every $r$-ball hypergraph $\mathcal{H}$ of $G$…

Bounded covering-packing conjecture. The class ${\mathcal M}_{\sf planar}$ has the bounded covering-packing property; equivalently, it satisfies the weak doubling property.