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On the Chromatic Number of the Visibility Graph of a Set of Points in the Plane
, 2005
"... The visibility graph V(P) of a point set P ⊆ 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 3chromatic visibility graphs. It is an open prob ..."
Abstract

Cited by 11 (3 self)
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The visibility graph V(P) of a point set P ⊆ 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 3chromatic 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 superpolynomial lower bound on the chromatic number (in terms of the clique number).