The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets
Abstract
The big-line-big-clique conjecture states that for all k,≥2 there is an integer n such that every finite set of at least n points in the plane contains collinear points or k pairwise visible points. We show that this conjecture is false for infinite point sets, by constructing a countably infinite point set with no 4 collinear points and no 3 pairwise visible points.
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