Visibility graphs of point sets in the plane

The visibility graph V(X) of a discrete point set X ⊂ R 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 graphG, there is a point setX ∈ R, such that the subgraph of V(X∪Z) 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 six settling a question by Kára, Pór and Wood.