具有大全角分辨率的图
Graphs with large total angular resolution
摘要：
直线图形的总角度分辨率是图形两条边之间的最小角度。它结合了有助于图形可读性的两个属性：角分辨率（入射边之间的最小角度）和交叉分辨率（交叉边之间的最小角度）。我们考虑一个图的全角分辨率，它是这个图的直线图的最大全角分辨率。我们证明了，直到有限个指定的例外的恒定大小，图的边数与$n$顶点和总角分辨率大于$60^{\circ}$是有界的$2n-6$。这个界限很紧.此外，我们表明，决定一个图是否有全角分辨率至少$60^{\circ}$是NP-困难的。
英文摘要：
The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the minimum angle between incident edges, and the crossing resolution, which is the minimum angle between crossing edges. We consider the total angular resolution of a graph, which is the maximum total angular resolution of a straight-line drawing of this graph. We prove that, up to a finite number of well specified exceptions of constant size, the number of edges of a graph with $n$ vertices and a total angular resolution greater than $60^{\circ}$ is bounded by $2n-6$. This bound is tight. In addition, we show that deciding whether a graph has total angular resolution at least $60^{\circ}$ is NP-hard.
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