We consider the problem of stretching pseudolines in a planar straight-line drawing to straight lines while preserving the straightness and the combinatorial embedding of the drawing. We answer open questions by Mchedlidze et al. by showing that not all instances with two pseudolines are stretchable. On the positive side, for $k\geq 2$ pseudolines intersecting in a single point, we prove that in case that some edge-pseudoline intersection-patterns are forbidden, all instances are stretchable. For intersection-free pseudoline arrangements we show that every aligned graph has an aligned drawing. This considerably reduces the gap between stretchable and non-stretchable instances.

中文翻译：

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可伸缩对齐图的表征

我们考虑将平面直线绘图中的伪线拉伸为直线的问题，同时保持绘图的直线度和组合嵌入。我们回答 Mchedlidze 等人的开放性问题。通过表明并非所有具有两条伪线的实例都是可拉伸的。从积极的方面来说，对于在单个点相交的 $k\geq 2$ 伪线，我们证明了在禁止某些边缘伪线相交模式的情况下，所有实例都是可拉伸的。对于无交叉的伪线排列，我们表明每个对齐的图形都有一个对齐的图形。这大大减少了可拉伸和不可拉伸实例之间的差距。