7 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…

Let $K_n$ have a convex drawing, and let $M$ be a plane matching, meaning a set of pairwise vertex-disjoint edges no two of which cross. Hoffmann–Tóth convex-matching conjecture. F…

$h$-convex crossed-edges conjecture. There exists an $h$-convex drawing of $K_n$ in which every edge is crossed.

Convex-drawing matching-avoidance conjecture. There exists a plane Hamiltonian cycle in $D$ that does not cross any edge of $M$.

Convex-drawing extension conjecture. Every plane Hamiltonian cycle $C$ in $D$ can be extended to a plane Hamiltonian subdrawing on $2n-3$ edges.

For a drawing $D$ of $K_n$, define its deficiency by … The drawing $D$ has the natural deficiency property if, for every vertex $v$ of $K_n$, … Here a convex drawing is a drawing i…

Let $D$ be an h-convex drawing of $K_n$, meaning that every induced subdrawing on $K_5$ is convex, and let $D[J]$ denote the subdrawing induced by an isomorph $J$ of $K_8$. The loc…