DeepAI AI Chat

Planar Point Sets Determine Many Pairwise Crossing Segments

04/18/2019

∙

by János Pach, et al.

∙

∙

We show that any set of n points in general position in the plane determines n^1-o(1) pairwise crossing segments. The best previously known lower bound, Ω(√(n)), was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.

János Pach
8 publications
Natan Rubin
5 publications
Gábor Tardos
5 publications

page 1

page 2

page 3

page 4

∙ 09/22/2021

On Crossing-Families in Planar Point Sets

A k-crossing family in a point set S in general position is a set of k s...

0 Oswin Aichholzer, et al. ∙

∙ 12/12/2018

The Crossing Tverberg Theorem

Tverberg's theorem is one of the cornerstones of discrete geometry. It s...

0 Radoslav Fulek, et al. ∙

∙ 02/09/2018

Colored ray configurations

We study the cyclic color sequences induced at infinity by colored rays ...

0 Ruy Fabila-Monroy, et al. ∙

∙ 06/01/2019

On problems related to crossing families

Given a set of points in the plane, a crossing family is a collection of...

0 William Evans, et al. ∙

∙ 02/26/2019

A new lower bound on the maximum number of plane graphs using production matrices

We use the concept of production matrices to show that there exist sets ...

0 Clemens Huemer, et al. ∙

∙ 03/30/2020

Long Alternating Paths Exist

Let P be a set of 2n points in convex position, such that n points are c...

0 Wolfgang Mulzer, et al. ∙

∙ 10/21/2022

On the Longest Flip Sequence to Untangle Segments in the Plane

A set of segments in the plane may form a Euclidean TSP tour or a matchi...

0 Guilherme D. da Fonseca, et al. ∙