The Chromatic Number of the Disjointness Graph of the Double Chain

Let P be a set of n >= 4 points in general position in the plane. Consider all the closed straight line segments with both endpoints in P. Suppose that these segments are colored with the rule that disjoint segments receive different colors. In this paper we show that if P is the point configuration known as the double chain, with k points in the upper convex chain and l >= k points in the lower convex chain, then k + l - left perpendicular root 2l + 1/4 - 1/2 right perpendicular colors are needed and that this number is sufficient.