In this paper, we study visibility representations of graphs that are embedded on a torus or a Klein bottle. Mohar and Rosenstiehl showed that any toroidal graph has a visibility representation on a flat torus bounded by a parallelogram, but left open the question whether one can assume a rectangular flat torus, i.e., a flat torus bounded by a rectangle. Independently the same question was asked by Tamassia and Tollis. We answer this question in the positive. With the same technique, we can also show that any graph embedded on a Klein bottle has a visibility representation on the rectangular flat Klein bottle.

翻译：在本文中,我们研究了嵌在横纹体或克莱因瓶子上的图形的可见度表示。Mohar和Rosenstiehl指出,任何类固醇图在被平行图层捆绑的平面上都有可见度表示,但对于是否可以假定矩形平面,即被矩形捆绑的平面,没有定论。Tamassia和Tollis单独提出了同样的问题。我们用正数回答这个问题。用同样的技术,我们还可以显示,嵌在克莱因瓶子上的任何图在矩形平板克莱因瓶上都有可见度表示。