Classification theorem for strong triangle blocking arrangements

Abstract

A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. We prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that n points in general position cannot be blocked by n-1 points, unless n = 2, 4. We also conjecture an extremal variant of the blocking points problem.