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Pré-Publication, Document De Travail Année : 2021

Intersection theorems for triangles

Résumé

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 $P$ of $n$ points is in convex position, then the largest intersecting family of triangles with vertices in $P$ contains at most $(\frac{1}{4}+o(1))\binom{n}{3}$ triangles.

Dates et versions

hal-03236558 , version 1 (26-05-2021)

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Peter Frankl, Andreas Holmsen, Andrey Kupavskii. Intersection theorems for triangles. 2021. ⟨hal-03236558⟩
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