### Abstract

The lattice diameter, ℓ(P), of a convex polygon P in R^{2} measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, w_{l}(P). We show, e.g., that w_{l} ≤ 4/3 ℓ + 1, thus giving a discrete analogue of Blaschke's theorem.

Original language | English |
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Pages (from-to) | 41-50 |

Number of pages | 10 |

Journal | Discrete Mathematics |

Volume | 241 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Oct 28 2001 |

### Fingerprint

### Keywords

- Convexity
- Covering minima
- Diameter
- Lattice

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*241*(1-3), 41-50. https://doi.org/10.1016/S0012-365X(01)00145-5

**On the lattice diameter of a convex polygon.** / Bárány, Imre; Füredi, Z.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 241, no. 1-3, pp. 41-50. https://doi.org/10.1016/S0012-365X(01)00145-5

}

TY - JOUR

T1 - On the lattice diameter of a convex polygon

AU - Bárány, Imre

AU - Füredi, Z.

PY - 2001/10/28

Y1 - 2001/10/28

N2 - The lattice diameter, ℓ(P), of a convex polygon P in R2 measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, wl(P). We show, e.g., that wl ≤ 4/3 ℓ + 1, thus giving a discrete analogue of Blaschke's theorem.

AB - The lattice diameter, ℓ(P), of a convex polygon P in R2 measures the longest string of integer points on a line contained in P. We relate the lattice diameter to the area and to the lattice width of P, wl(P). We show, e.g., that wl ≤ 4/3 ℓ + 1, thus giving a discrete analogue of Blaschke's theorem.

KW - Convexity

KW - Covering minima

KW - Diameter

KW - Lattice

UR - http://www.scopus.com/inward/record.url?scp=0035965428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035965428&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(01)00145-5

DO - 10.1016/S0012-365X(01)00145-5

M3 - Article

AN - SCOPUS:0035965428

VL - 241

SP - 41

EP - 50

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -