The maximum chromatic number of the disjointness graph of segments on n-point sets in the plane with \(n\le 16\)

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 \(\chi (D(P))\) $\chi (D(P))$ to denote the chromatic number of D(P), and use d(n) to denote the maximum \(\chi (D(P))\) $\chi (D(P))$ taken over all sets P of n points in general position in the plane. In this paper, we show that \(d(n)=n-2\) $d(n)=n-2$ if and only if \(n\in \{3,4,\ldots ,16\}\) $n\in \{3,4,\dots ,16\}$ .