Width-diameter relations for planar convex sets with lattice point constraints

被引：1

作者：

Awyong, PW ^{[1
]}

Scott, PR ^{[1
]}

机构：

[1] UNIV ADELAIDE,DEPT PURE MATH,ADELAIDE,SA 5005,AUSTRALIA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 1996年 / 53卷 / 03期

关键词：

D O I：

10.1017/S0004972700017238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an inequality concerning the width and diameter of a planar convex set with interior containing no point of the rectangular lattice. We then use the result to obtain a corresponding inequality for a planar convex set with interior containing exactly two points of the integral lattice.

引用

页码：469 / 478

页数：10

共 49 条

[31] ON THE WIDTH OF A PLANAR CONVEX SET CONTAINING ZERO OR ONE LATTICE POINTS
SCOTT, PR
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1993, 48 (01) : 47 - 53
[32] CONVEX INDEPENDENT SETS AND 7-HOLES IN RESTRICTED PLANAR POINT SETS
VALTR, P
DISCRETE & COMPUTATIONAL GEOMETRY, 1992, 7 (02) : 135 - 152
[33] COUNTING CONVEX KAPPA-GONS IN PLANAR POINT SETS
ROTE, G
WOEGINGER, G
INFORMATION PROCESSING LETTERS, 1992, 41 (04) : 191 - 194
[34] Planar point sets with a small number of empty convex polygons
Bárány, I
Valtr, P
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2004, 41 (02) : 243 - 266
[35] The isodiametric problem for lattice-point-free convex sets
M. A. Hernández Cifre
S. Vassallo
Acta Mathematica Hungarica, 2007, 114 : 337 - 355
[36] The isodiametric problem for lattice-point-free convex sets
Hernandez Cifre, M. A.
Vassallo, S.
ACTA MATHEMATICA HUNGARICA, 2007, 114 (04) : 337 - 355
[37] ON THE AREA OF PLANAR CONVEX-SETS CONTAINING MANY LATTICE POINTS
SCOTT, PR
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1987, 35 (03) : 441 - 454
[38] AREA-DIAMETER AND AREA-WIDTH RELATIONS FOR COVERING PLANE SETS
VASSALLO, S
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1995, 51 (01) : 163 - 169
[39] An Analysis of Mixed Integer Linear Sets Based on Lattice Point Free Convex Sets
Andersen, Kent
Louveaux, Quentin
Weismantel, Robert
MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (01) : 233 - 256
[40] Linear-size planar Manhattan network for convex point sets
Jana, Satyabrata
Maheshwari, Anil
Roy, Sasanka
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2022, 100

← 1 2 3 4 5 →