5 Colorable Visibility Graphs Have Bounded Size or 4 Collinear Points
Combinatorics
2014-10-28 v1
Abstract
We investigate the question of finding a bound for the size of a -colorable finite visibility graph that has at most collinear points. This can be regarded as a relaxed version of the Big Line - Big Clique conjecture. We prove that any finite point set that has at least 2311 points has either 4 collinear points or a visibility graph that cannot be 5-colored.
Cite
@article{arxiv.1410.7273,
title = {5 Colorable Visibility Graphs Have Bounded Size or 4 Collinear Points},
author = {Bálint Hujter and Sándor Kisfaludi-Bak},
journal= {arXiv preprint arXiv:1410.7273},
year = {2014}
}
Comments
11+6 pages