The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets

Attila~P\'or; David R. Wood

arxiv: 1008.2988 · v1 · pith:R5CBWEH2new · submitted 2010-08-18 · 🧮 math.CO

The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets

Attila~P\'or , David R. Wood This is my paper

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keywords pointsconjectureinfinitepointbig-line-big-cliquecollinearfalsepairwise

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The big-line-big-clique conjecture states that for all $k,\ell\geq2$ there is an integer $n$ such that every finite set of at least $n$ points in the plane contains $\ell$ 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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