On the Number of Hyperedges in the Hypergraph of Lines and Pseudo-Discs

Chaya Keller; Balázs Keszegh; Dömötör Pálvölgyi

doi:10.37236/10424

On the Number of Hyperedges in the Hypergraph of Lines and Pseudo-Discs

Chaya Keller, Balázs Keszegh, Dömötör Pálvölgyi

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Consider a 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(n²) and that the total number of hyperedges is bounded by O(n³). Both bounds are tight.

Original language	English
Article number	P3.25
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	3
DOIs	https://doi.org/10.37236/10424
State	Published - 2022

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abstract = "Consider a 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 Ot(n2) and that the total number of hyperedges is bounded by O(n3). Both bounds are tight.",

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On the Number of Hyperedges in the Hypergraph of Lines and Pseudo-Discs

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