The angular resolution of a planar straight-line drawing of a graph is the smallest angle formed by two edges incident to the same vertex. Garg and Tamassia (ESA '94) constructed a family of planar graphs with maximum degree $d$ that have angular resolution $O((\log d)^{\frac{1}{2}}/d^{\frac{3}{2}})$ in any planar straight-line drawing. This upper bound has been the best known upper bound on angular resolution for a long time. In this paper, we improve this upper bound. For an arbitrarily small positive constant $\varepsilon$, we construct a family of planar graphs with maximum degree $d$ that have angular resolution $O((\log d)^\varepsilon/d^{\frac{3}{2}})$ in any planar straight-line drawing.

翻译：平面直线图绘制的角度分辨率是指与同一顶点相关联的两条边所形成的最小角度。Garg 和 Tamassia (ESA '94) 构造了一个最大度为 $d$ 的平面图族，其在任意平面直线绘制中角度分辨率均为 $O((\log d)^{\frac{1}{2}}/d^{\frac{3}{2}})$。长期以来，这一上界一直是角度分辨率已知的最佳上界。本文改进了该上界：对于任意足够小的正常数 $\varepsilon$，我们构造了一个最大度为 $d$ 的平面图族，其在任意平面直线绘制中角度分辨率均为 $O((\log d)^\varepsilon/d^{\frac{3}{2}})$。