Cell-paths in mono- And bichromatic line arrangements in the plane

Oswin Aichholzer; Jean Cardinal; Thomas Hackl; Ferran Hurtado; Matias Korman; Alexander Pilz; Rodrigo I. Silveira; Ryuhei Uehara; Pavel Valtr; Birgit Vogtenhuber; Emo Welzl

Cell-paths in mono- And bichromatic line arrangements in the plane

Oswin Aichholzer, Jean Cardinal, Thomas Hackl, Ferran Hurtado, Matias Korman, Alexander Pilz, Rodrigo I. Silveira, Ryuhei Uehara, Pavel Valtr, Birgit Vogtenhuber, Emo Welzl

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

2 Citations (Scopus)

Abstract

We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n²/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.

Original language	English
Pages (from-to)	317-332
Number of pages	16
Journal	Discrete Mathematics and Theoretical Computer Science
Volume	16
Issue number	3
Publication status	Published - 2014
Externally published	Yes

Keywords

Discrete geometry
Hamiltonicity
Line arrangement
Planar graphs

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)
Discrete Mathematics and Combinatorics

Cite this

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abstract = "We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.",

keywords = "Discrete geometry, Hamiltonicity, Line arrangement, Planar graphs",

author = "Oswin Aichholzer and Jean Cardinal and Thomas Hackl and Ferran Hurtado and Matias Korman and Alexander Pilz and Silveira, {Rodrigo I.} and Ryuhei Uehara and Pavel Valtr and Birgit Vogtenhuber and Emo Welzl",

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language = "English",

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TY - JOUR

T1 - Cell-paths in mono- And bichromatic line arrangements in the plane

AU - Aichholzer, Oswin

AU - Cardinal, Jean

AU - Hackl, Thomas

AU - Hurtado, Ferran

AU - Korman, Matias

AU - Pilz, Alexander

AU - Silveira, Rodrigo I.

AU - Uehara, Ryuhei

AU - Valtr, Pavel

AU - Vogtenhuber, Birgit

AU - Welzl, Emo

PY - 2014

Y1 - 2014

N2 - We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.

AB - We prove that the dual graph of any arrangement of η lines in general position always contains a path of length at least n2/4. Further, we show that in every arrangement of η red and blue lines-in general position and not all of the same color-there is a simple path through at least η cells where red and blue lines are crossed alternatingly.

KW - Discrete geometry

KW - Hamiltonicity

KW - Line arrangement

KW - Planar graphs

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UR - http://www.scopus.com/inward/citedby.url?scp=84919952304&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84919952304

VL - 16

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EP - 332

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

IS - 3

ER -

Cell-paths in mono- And bichromatic line arrangements in the plane

Abstract

Keywords

ASJC Scopus subject areas

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