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.
- Covering minima
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics