可拉伸对齐图的一个刻画
Towards a characterization of stretchable aligned graphs
摘要：
我们考虑在保持直线度和组合嵌入的情况下，将平面直线图中的伪线拉伸为直线的问题。我们回答了Mchedlidze等人提出的开放性问题。通过证明并非所有具有两个伪线的实例都是可拉伸的。在积极的一面，对于$k\geq 2$伪线相交于一个点，我们证明了在一些边伪线相交模式是禁止的情况下，所有的实例是可拉伸的。对于无交叉的伪线安排，我们表明，每一个对齐的图有对齐的图纸。这大大减少了可拉伸和不可拉伸实例之间的差距。
英文摘要：
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.
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