Let $P$ be a set of $n$ points in general and convex position in the plane. Let $D_n$ be the graph whose vertex set is the set of all line segments with endpoints in $P$, where disjoint segments are adjacent. The chromatic number of this graph was first studied by Araujo et al. [\emph{CGTA}, 2005]. The previous best bounds are $\frac{3n}{4}\leq\chi(D_n) <n-\sqrt{\frac{n}{2}}$ (ignoring lower order terms). In this paper we improve the lower bound to $\chi(D_n)\geq n-\sqrt{2n}$, to conclude a near-tight bound on $\chi(D_n)$.
翻译：让 $P 成为平面上一般的 $n 点和 convex 位置的一套 。 请将 $_n 表示顶点是所有线段的组合, 端点为 $P, 端点为 $P, 断开的段相邻 。 此图的染色号由 Araujo et al. [\emph{ CGTA}, 2005] 首次研究 。 上一个最好的边框是 $\ frac{ 3n}4 ⁇ leq\chi (D_ n) <n\ sqrt\ frac{n\\\\\\\\\\\\\\\\\ \ \ \ \ $( \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\\\\\\\\\ \ \\\\\\\\\\\\\\ \\\\\\\ \ \ \ \ \ \ \\\\\ \ \ \ \ \ \ \ \ \ \ \\\ \ \ \ \\\\\\\ \ \ \ \\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
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