3 problems

An h-convex drawing of $K_n$ is a drawing in which the vertices are in convex position with respect to the relevant hull structure. H-convex all-edges-crossed conjecture. For…

A simple drawing of $K_n$ is crossing-maximal if it has $\binom{n}{4}$ crossings; an uncrossed edge is an edge crossed by no other edge. Harborth–Mengersen's conjecture. Every cros…

Let $S$ be a point set in the plane in general position, and let a longest Hamiltonian cycle be a Hamiltonian cycle on $S$ whose total edge length is maximal. Longest-cycle crossin…