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

02/23/2021

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by   Chaya Keller, et al.

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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.