Let $P$ be a set of $n\geq 4$ 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 $l \ge k$ points in the lower convex chain, then $k+l- \left\lfloor \sqrt{ 2l+\frac{ 1}{ 4}} - \frac{ 1}{ 2}\right\rfloor$ colors are needed and that this number is sufficient.
Categories: math.CO