### 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 |

### Keywords

- Convexity
- Covering minima
- Diameter
- Lattice

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Bárány, I., & Füredi, Z. (2001). On the lattice diameter of a convex polygon.

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