8 problems

Given a graph $G$, let its obstacle number be the minimum number of faces in a straight-line drawing whose union intersects every non-edge, and let $f(h,n)$ denote the number of…

Let $\operatorname{obs}(n)$ denote the maximum obstacle number over all graphs on $n$ vertices. Mukkamala–Pach–Pálvölgyi's conjecture. The maximum obstacle number of $n$-vertex gra…

Let $G$ be a graph with at most $10$ vertices. Let $\operatorname{obs}_{\mathrm{in}}(G)$ be the number of obstacles needed to represent $G$ in the absence of outside obstacles, and…

Let $G$ be a graph whose circumference is at most $7$, where the circumference is the length of a longest cycle in $G$. An outside-obstacle representation represents $G$ as a visib…

Let $G$ be a graph, let $\operatorname{obs}(G)$ be the smallest number of obstacles needed to represent $G$ as a visibility graph, and let $\operatorname{obs}_{\mathrm{out}}(G)$ be…

Let $G$ be a graph. Write $\operatorname{obs}(G)$ for the smallest number of obstacles needed to represent $G$ as a visibility graph, and let $\operatorname{obs}_{\mathrm{out}}(G)$…

Obstacle-number graph-counting conjecture. The number of such graphs satisfies

For a graph $G$, the convex obstacle number is the smallest number of convex polygonal obstacles in an obstacle representation of $G$, while the disjoint convex obstacle number is…