Abstract
The visibility graph \(\mathcal {V}(X)\) of a discrete point set X⊂ℝ2 has vertex set X and an edge xy for every two points x,y∈X whenever there is no other point in X on the line segment between x and y. We show that for every graph G, there is a point set X∈ℝ2, such that the subgraph of \(\mathcal {V}(X\cup \mathbb {Z}^{2})\) induced by X is isomorphic to G. As a consequence, we show that there are visibility graphs of arbitrary high chromatic number with clique number 6 settling a question by Kára, Pór and Wood.
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Supported by the DFG Research Center Matheon (FZT86).
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Pfender, F. Visibility Graphs of Point Sets in the Plane. Discrete Comput Geom 39, 455–459 (2008). https://doi.org/10.1007/s00454-008-9056-z
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DOI: https://doi.org/10.1007/s00454-008-9056-z