The sylvester-chvatal theorem

被引：12
|
作者：
Chen, XM [1 ]
机构：
[1] Rutgers State Univ, Dept Comp Sci, Piscataway, NJ 08854 USA
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2006年 / 35卷 / 02期
关键词：
Computational Mathematic; Euclidean Space; Present Article;
D O I：
10.1007/s00454-005-1216-9
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The Sylvester-Gallai theorem asserts that every finite set S of points in two-dimensional Euclidean space includes two points, a and b, such that either there is no other point in S on the line ab, or the line ab contains all the points in S. Chvatal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. In the present article we prove this conjecture.
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页码：193 / 199
页数：7
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