AI Chat AI Image Generator AI Video Text to Speech

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

02/23/2021

∙

by Chaya Keller, et al.

∙

∙

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.

Chaya Keller
10 publications
Balázs Keszegh
13 publications
Dömötör Pálvölgyi
16 publications

page 1

page 2

page 3

page 4

research

∙ 01/23/2020

Arrangements of Approaching Pseudo-Lines

We consider arrangements of n pseudo-lines in the Euclidean plane where ...

0 Stefan Felsner, et al. ∙

research

∙ 02/24/2018

On Pseudo-disk Hypergraphs

Let F be a family of pseudo-disks in the plane, and P be a finite subset...

0 Boris Aronov, et al. ∙

research

∙ 06/11/2018

Plane drawings of the generalized Delaunay-graphs for pseudo-disks

We study general Delaunay-graphs, which are a natural generalizations of...

0 Balázs Keszegh, et al. ∙

research

∙ 09/17/2018

A new lower bound on Hadwiger-Debrunner numbers in the plane

A set family F is said to satisfy the (p,q) property if among any p sets...

0 Chaya Keller, et al. ∙

research

∙ 12/28/2022

Hypergraphs with Polynomial Representation: Introducing r-splits

Inspired by the split decomposition of graphs and rank-width, we introdu...

0 Mohammed Haddad, et al. ∙

research

∙ 03/01/2020

The Maximum-Level Vertex in an Arrangement of Lines

Let L be a set of n lines in the plane, not necessarily in general posit...

0 Dan Halperin, et al. ∙

research

∙ 02/27/2023

The Complexity of Recognizing Geometric Hypergraphs

As set systems, hypergraphs are omnipresent and have various representat...

0 Daniel Bertschinger, et al. ∙