Abstract:
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.