All Questions

Consider a drawing (in $\mathbb{R}^2$) of a planar graph. (The drawing is given, contrarily to the common setup in graph theory where we are seeking to build a drawing with specific properties.) For ...

Let $P$ be a convex polygon. Suppose every interior angle of $P$ is obtuse. Is it always the case that there exist three vertices $p, q, r$ of $P$ such that $\triangle pqr$ is acute? I conjecture ...