A note on geometric 3-hypergraphs [article]

Andrew Suk
2011 arXiv   pre-print
In this note, we prove several Turán-type results on geometric hypergraphs. The two main theorems are 1) Every n-vertex geometric 3-hypergraph in 2-space with no three strongly crossing edges has at most O(n^2) edges, 2) Every n-vertex geometric 3-hypergraph in 3-space with no two disjoint edges has at most O(n^2) edges. These results support two conjectures that were raised by Dey and Pach, and by Akiyama and Alon.
arXiv:1010.5716v3 fatcat:dic67fwnlbgh5kvyglgjz726rq