On the connectivity of the disjointness graph of segments of point sets in general position in the plane

Let P be a set of n ≥ 3 points in general position in the plane. The edge disjointness graph D(P) of P is the graph whose vertices are all the closed straight line segments with endpoints in P, two of which are adjacent in D(P) if and only if they are disjoint. We show that the connectivity of D(P) is at least ^(bn−₂^{2 2 c)} + ^(dn−₂^{2 2 e)}, and that this bound is tight for each n ≥ 3.