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arXiv · 1410.7273

5 Colorable Visibility Graphs Have Bounded Size or 4 Collinear Points

Bálint Hujter·Sándor Kisfaludi-Bak
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Abstract

We investigate the question of finding a bound for the size of a $χ$-colorable finite visibility graph that has at most $\ell$ 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.

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Bálint Hujter, Sándor Kisfaludi-Bak. 2014-10-27. 5 Colorable Visibility Graphs Have Bounded Size or 4 Collinear Points. https://arxiv.org/abs/1410.7273

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