DIMACS TR: 2003-32

The Sylvester-Chvatal Theorem

Author: Xiaomin Chen


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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