## DIMACS TR: 2003-32

## The Sylvester-Chvatal Theorem

### Author: Xiaomin Chen

**
ABSTRACT
**

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 $S$
is on the line $ab$, or the line $ab$ contains all the points in $S$.
V. Chv\'{a}tal 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 to be true.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2003/2003-32.ps.gz

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