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5 Colorable Visibility Graphs Have Bounded Size or 4 Collinear Points

2014/10/27 by Bálint Hujter, Hujter, Bálint, Sándor Kisfaludi-Bak +2
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1410.7273

11+6 pages

arxiv created 2014/10/27 · openalex publication_date 2014/10/27 · arxiv updated 2014/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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