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

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

2010-08-18

arxiv.org/abs/1008.2988v1

Mathematics

Combinatorics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-503787