Let P be a finite set of points in general position in the plane. The
disjointness graph of segments 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. As usual, we use
χ(D(P)) to denote the chromatic number of D(P), and use d(n) to denote
the maximum χ(D(P)) taken over all sets P of n points in general
position in the plane. In this paper we show that d(n)=n−2 if and only if
n∈{3,4,…,16}.Comment: 25 pages, 3 figure