On the lattice diameter of a convex polygon

Imre Bárány, Zoltán Füredi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)41-50
Number of pages10
JournalDiscrete Mathematics
Volume241
Issue number1-3
DOIs
Publication statusPublished - Oct 28 2001

Keywords

  • Convexity
  • Covering minima
  • Diameter
  • Lattice

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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