—We say that two edges in the hypercube are close if their endpoints form a 2-dimensional subcube. We consider the problem of constructing a 2-factor not containing close edges in the hypercube graph. For solving this problem,we use the new construction for building 2-factors which generalizes the previously known stream construction for Hamiltonian cycles in a hypercube.Owing to this construction, we create a family of 2-factors without close edges in cubes of all dimensions starting from 10, where the length of the cycles in the obtained 2-factors grows together with the dimension.

中文翻译：

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n维立方体中没有闭合边的2因子

—我们说，如果超立方体中的两个端点形成二维子立方体，则它们的边缘会闭合。我们考虑在超立方体图中构造不包含闭合边的2因子问题。为解决此问题，我们使用了新的构造2因子的构造，该构造对超立方体中哈密顿循环的先前已知的流构造进行了概括。由于这种构造，我们创建了2因子族，在所有尺寸的立方体中都没有闭合边从10开始，获得的2因子中的循环长度与尺寸一起增长。