We study the problem of drawing simultaneously embedded graphs with few bends. We show that for any simultaneous embedding with fixed edges (Sefe) of two graphs, there exists a corresponding drawing realizing this embedding such that common edges are drawn as straight-line segments and each exclusive edge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (Sge) for a non-trivial class of graphs.

中文翻译：

---

同时绘制带有少量弯曲的嵌入图

我们研究了同时绘制具有少量弯曲的嵌入图的问题。我们表明，对于两个图的任何具有固定边 ( Sefe ) 的同时嵌入，存在实现此嵌入的相应绘图，使得公共边被绘制为直线段，并且每个排他边具有恒定数量的弯曲。如果公共图是双连通和诱导的，则存在直线图。这产生了第一个有效的同时几何嵌入 ( Sge ) 测试算法，用于一类非平凡的图。