A Note on Geometric 3-Hypergraphs

Andrew Suk ()
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Andrew Suk: Massachusetts Institute of Technology, Department of Mathematics

A chapter in Thirty Essays on Geometric Graph Theory, 2013, pp 489-498 from Springer

Abstract: Abstract 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 the plane with no three strongly crossing edges has at most O(n 2) edges, and (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.

Keywords: Geometric Hypergraphs; Edge Disjoint; Rightmost Intersection; Colored Tverberg Theorem; Fractional Helly Theorem (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-0110-0_26

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DOI: 10.1007/978-1-4614-0110-0_26

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