A note on coloring line arrangements

Eyal Ackerman; János Pach; Rom Pinchasi; Radoš Radoičić; Géza Tóth

doi:10.37236/2660

A note on coloring line arrangements

Eyal Ackerman, János Pach, Rom Pinchasi, Radoš Radoičić, Géza Tóth

Faculty of Natural Sciences

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

Abstract

We show that the lines of every arrangement of n lines in the plane can be colored with O colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a Θ(logn√) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdo{double acute}s: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

Original language	English
Journal	Electronic Journal of Combinatorics
Volume	21
Issue number	2
DOIs	https://doi.org/10.37236/2660
State	Published - 9 May 2014

Keywords

Arrangements of lines
Chromatic number
Sparse hypergraphs

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/2660

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AU - Ackerman, Eyal

AU - Pach, János

AU - Pinchasi, Rom

AU - Radoičić, Radoš

AU - Tóth, Géza

PY - 2014/5/9

Y1 - 2014/5/9

N2 - We show that the lines of every arrangement of n lines in the plane can be colored with O colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a Θ(logn√) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdo{double acute}s: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

AB - We show that the lines of every arrangement of n lines in the plane can be colored with O colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a Θ(logn√) factor. Any further improvement on this bound would also improve the best known lower bound on the following problem of Erdo{double acute}s: estimate the maximum number of points in general position within a set of n points containing no four collinear points.

KW - Arrangements of lines

KW - Chromatic number

KW - Sparse hypergraphs

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A note on coloring line arrangements

Abstract

Keywords

ASJC Scopus subject areas

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