We approach the cycle double cover conjecture by looking for a circular 2-cell embedding of cubic graphs on an arbitrary surface. It is easy to see that if such an embedding exists, we can get to it from an arbitrary starting 2-cell embedding by repeating ``twists of an edge''. We study this twisting operation in detail and deduce bounds on the number of singular edges (edges where a face meets itself).

翻译：我们通过寻找任意曲面上三次图的圆形2-胞腔嵌入来探讨圈双覆盖猜想。易见，若此类嵌入存在，可通过重复执行“边扭转”操作，从任意初始2-胞腔嵌入出发得到目标嵌入。我们详细研究这一扭转操作，并推导出奇异边（即面与自身相交的边）数量的上界。