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.
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Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 3, pp. 5–26.
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Bykov, I.S. 2-Factors Without Close Edges in the n-Dimensional Cube. J. Appl. Ind. Math. 13, 405–417 (2019). https://doi.org/10.1134/S1990478919030037
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DOI: https://doi.org/10.1134/S1990478919030037