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

Authors:
Jan Kára;Attila Pór;David R. Wood
Affiliations:
Department of Applied Mathematics, Charles University, 118 00 Prague 1, Czech Republic;Department of Applied Mathematics, Charles University, 118 00 Prague 1, Czech Republic;Departament de Matematica Aplicada II, Universitat Politecnica de Catalunya, E-08034 Barcelona, Spain
Venue:
Discrete & Computational Geometry
Year:
2005

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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).