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 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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Chen, X. The Sylvester-Chvatal Theorem. Discrete Comput Geom 35, 193–199 (2006). https://doi.org/10.1007/s00454-005-1216-9
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DOI: https://doi.org/10.1007/s00454-005-1216-9