The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets
Combinatorics
2010-08-19 v1
Abstract
The big-line-big-clique conjecture states that for all there is an integer such that every finite set of at least points in the plane contains collinear points or 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.
Keywords
Cite
@article{arxiv.1008.2988,
title = {The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets},
author = {Attila~Pór and David R. Wood},
journal= {arXiv preprint arXiv:1008.2988},
year = {2010}
}