We show that every outerplanar graph can be linearly embedded in the plane such that the number of distinct distances between pairs of adjacent vertices is at most thirteen and there is no intersection between the image of a vertex and that of an edge not containing it.

This extends the work of Alon and the second author, where only overlap between vertices was disallowed, thus settling a problem posed by Carmi, Dujmović, Morin and Wood.

中文翻译：

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使用十三个边长绘制外平面图

我们表明，每个外平面图都可以线性嵌入平面中，使得相邻顶点对之间的不同距离的数量最多为 13，并且顶点的图像与不包含它的边的图像之间没有交集。

这扩展了 Alon 和第二作者的工作，其中只不允许顶点之间的重叠，从而解决了 Carmi、Dujmović、Morin 和 Wood 提出的问题。