On the lattice diameter of a convex polygon

Imre Bárány, Z. 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

Fingerprint

Convex polygon
Integer Points
Strings
Analogue
Line
Theorem

Keywords

  • Convexity
  • Covering minima
  • Diameter
  • Lattice

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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

In: Discrete Mathematics, Vol. 241, No. 1-3, 28.10.2001, p. 41-50.

Research output: Contribution to journalArticle

Bárány, Imre ; Füredi, Z. / On the lattice diameter of a convex polygon. In: Discrete Mathematics. 2001 ; Vol. 241, No. 1-3. pp. 41-50.
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