### Abstract

We show how to construct an arrangement of n lines having a monotone path of length Ω(n^{2-(d/√logn}), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

Original language | English (US) |
---|---|

Pages (from-to) | 167-176 |

Number of pages | 10 |

Journal | Discrete and Computational Geometry |

Volume | 32 |

Issue number | 2 |

State | Published - 2004 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Discrete and Computational Geometry*,

*32*(2), 167-176.

**Long monotone paths in line arrangements.** / Balogh, József; Regev, Oded; Smyth, Clifford; Steiger, William; Szegedy, Mario.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 32, no. 2, pp. 167-176.

}

TY - JOUR

T1 - Long monotone paths in line arrangements

AU - Balogh, József

AU - Regev, Oded

AU - Smyth, Clifford

AU - Steiger, William

AU - Szegedy, Mario

PY - 2004

Y1 - 2004

N2 - We show how to construct an arrangement of n lines having a monotone path of length Ω(n2-(d/√logn), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

AB - We show how to construct an arrangement of n lines having a monotone path of length Ω(n2-(d/√logn), where d > 0 is some constant, and thus nearly settle the long standing question on monotone path length in line arrangements.

UR - http://www.scopus.com/inward/record.url?scp=4344580535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4344580535&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 167

EP - 176

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 2

ER -