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arXiv 2608.19468math.COcs.DM

大型有限点集包含4个共线点或6个团

Large Finite Point Sets Have 4 Collinear Points or a 6-Clique

Édouard Bonnet

AI总结:

该研究证明大小不小于10^11055931的有限点集必含4个共线点或6个两两可见点,解决了大线大团猜想的首个公开情况

AI中文摘要:

我们证明,每个大小至少为10^11055931的有限点集,要么有4个共线点,要么有6个两两可见的点,这解决了Kára、Pór和Wood提出的大线大团猜想的首个公开情况

英文摘要:

We prove that every finite point set of size at least $10^{11055931}$ has four collinear points or six points that pairwise see each other. This resolves the first open case of the big-line-big-clique conjecture of Kára, Pór, and Wood.

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