3 problems

Let $X$ denote the set of crossing points and $T$ the set of tangency points in a family of $n$ closed curves such that every pair of curves intersects. Richter–Thomassen conjectur…

Let a family of planar curves be precisely 1-intersecting if every pair of curves has precisely one common point, either a crossing or a tangency, and assume that no three curves s…

Let $\mathcal{C}_{1},\mathcal{C}_{2} \subset \mathbb{P}^{2}_{\mathbb{C}}$ be two $d$-arrangements for a fixed $d\geqslant 1$. Let $G_{1}$ and $G_{2}$ be their associated Levi graph…