The distance between two vertices of a polytope is the minimum number of edges in a path joining them. The diameter of a polytope is the greatest distance between two vertices of the polytope. We show that if P is a d-dimensional polytope with n facets, then the diameter of P is at most $ $-3(,r -d
✦ LIBER ✦
An upper bound for the minimum diameter of integral point sets
✍ Scribed by Heiko Harborth; Arnfried Kemnitz; Meinhard Möller
- Publisher
- Springer
- Year
- 1993
- Tongue
- English
- Weight
- 243 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0179-5376
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In this paper, we establish improved upper bounds on the size of integral solutions to hyper- and super-elliptic equations under the conditions of LeVeque (Acta. Arith. IX (1964), 209-219). The proof follows the classical argument of Siegel (J. London Math. Soc. 1 (1926), 66-68), using upper bounds