Classification theorem for strong triangle blocking arrangements

TL;DR

This paper classifies strong triangle blocking arrangements, a geometric configuration related to blocking sets, and provides a new proof for a known result about point blocking in general position.

Contribution

It establishes a classification theorem for strong triangle blocking arrangements and applies it to reprove a key result in blocking points in geometric configurations.

Findings

Classification theorem for strong triangle blocking arrangements

New proof of the blocking points result by Ackerman et al.

Conjecture on an extremal variant of the blocking points problem

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. Our aim in this paper is to 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.