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

Cell-paths in mono- And bichromatic line arrangements in the plane. / Aichholzer, Oswin; Cardinal, Jean; Hackl, Thomas; Hurtado, Ferran; Korman, Matias; Pilz, Alexander; Silveira, Rodrigo I.; Uehara, Ryuhei; Valtr, Pavel; Vogtenhuber, Birgit; Welzl, Emo.

In: Discrete Mathematics and Theoretical Computer Science, Vol. 16, No. 3, 2014, p. 317-332.

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

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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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IS - 3

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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