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Intersection theorems for triangles

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 نشر من قبل Andrey Kupavskii
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
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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.



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