Blocking Delaunay triangulations

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex position, [Formula: see text] white points are always sufficient to block it, and (iii) at least [Formula: see text] white points are always necessary to block a set of n black points.