论文标题
成对三角形的极端问题
Extremal problems for pairs of triangles
论文作者
论文摘要
凸几何超图或CGH由平面中严格凸点集的子集组成。有八个成对的非构形CGH，由两个不相交的三元组组成。这些由Braß（2004）和Aronov，Dujmović，Morin，Ooms和Da Silveira（2019）详细研究。我们为八个配置中的七个确切确定极端函数。 以上结果是关于周期有序的超图。我们将其中的一些扩展到带有非凸线的顶点的三角系统。我们还解决了P. Frankl，Holmsen和Kupavskii（尤其是2020年）提出的问题，我们确定了一个相交三角形家族的确切最大大小，其顶点来自飞机上的一组$ n $点。
A convex geometric hypergraph or cgh consists of a family of subsets of a strictly convex set of points in the plane. There are eight pairwise nonisomorphic cgh's consisting of two disjoint triples. These were studied at length by Braß (2004) and by Aronov, Dujmović, Morin, Ooms, and da Silveira (2019). We determine the extremal functions exactly for seven of the eight configurations. The above results are about cyclically ordered hypergraphs. We extend some of them for triangle systems with vertices from a non-convex set. We also solve problems posed by P. Frankl, Holmsen and Kupavskii (2020), in particular, we determine the exact maximum size of an intersecting family of triangles whose vertices come from a set of $n$ points in the plane.
