Intersection theorems for triangles
Combinatorics
2021-02-19 v2 Discrete Mathematics
Abstract
Given a family of sets on the plane, we say that the family is intersecting if for any two sets from the family their interiors intersect. In this paper, we study intersecting families of triangles with vertices in a given set of points. In particular, we show that if a set of points is in convex position, then the largest intersecting family of triangles with vertices in contains at most triangles.
Cite
@article{arxiv.2009.14560,
title = {Intersection theorems for triangles},
author = {Peter Frankl and Andreas Holmsen and Andrey Kupavskii},
journal= {arXiv preprint arXiv:2009.14560},
year = {2021}
}