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On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane

Abstract

The visibility graph V(P) of a point set P \subseteq R2 has vertex set P, such that two points v,w ∈ P are adjacent whenever there is no other point in P on the line segment between v and w. We study the chromatic number of V(P). We characterise the 2- and 3-chromatic visibility graphs. It is an open problem whether the chromatic number of a visibility graph is bounded by its clique number. Our main result is a super-polynomial lower bound on the chromatic number (in terms of the clique number).

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Correspondence to Jan Kára, Attila Pór or David R. Wood.

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Kára, J., Pór, A. & Wood, D. On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane. Discrete Comput Geom 34, 497–506 (2005). https://doi.org/10.1007/s00454-005-1177-z

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  • DOI: https://doi.org/10.1007/s00454-005-1177-z

Keywords

  • Computational Mathematic
  • Line Segment
  • Open Problem
  • Chromatic Number
  • Visibility Graph