6 problems

Linear distinct-dot-products conjecture. For every such sequence,

Payne–Wood's coloring conjecture. Every such set $P$ can be colored with $O(\sqrt{n})$ colors so that each color class is in general position.

Payne–Wood's conjecture.

Let $S$ be a set of $n$ points in the Euclidean plane in general position, meaning that no three points of $S$ are collinear. A crossing family is a set of segments spanned by poin…

Let $S$ be a set of $n$ points in the Euclidean plane in general position, meaning that no three points of $S$ are collinear. A segment of $S$ is a line segment whose endpoints are…

Let $f(n)$ be the minimum number of segments such that every set of $n$ points in the plane can be covered by a possibly self-intersecting polygonal path, and let $g(n)$ be the min…