$2$-Factors without close edges in the $n$-dimensional cube

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. Tab. 5, bibliogr. 12.