Direction trees
A direction tree for a finite set X of points in the plane is a tree T whose vertices are the points of X such that any two edges of T determine lines with different slopes. Ungar's theorem says that any n noncollinear points in the real affine plane determine at least different n-1 slopes among connecting lines. This note uses Ungar's theorem plus Hall's theorem on distinct representatives to prove the existence of a direction tree for any finite set of noncollinear points.
scientific article; zbMATH DE number 3995709
scientific article