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arXiv · 2102.11937

On the number of hyperedges in the hypergraph of lines and pseudo-discs

Chaya Keller·Balázs Keszegh·Dömötör Pálvölgyi
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Abstract

Consider the hypergraph whose vertex set is a family of $n$ lines in general position in the plane, and whose hyperedges are induced by intersections with a family of pseudo-discs. We prove that the number of $t$-hyperedges is bounded by $O_t(n^2)$ and that the total number of hyperedges is bounded by $O(n^3)$. Both bounds are tight.

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Chaya Keller, Balázs Keszegh, Dömötör Pálvölgyi. 2022-08-25. On the number of hyperedges in the hypergraph of lines and pseudo-discs. https://arxiv.org/abs/2102.11937

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