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 p...

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Bibliographic Details
Published in:	Journal of applied and industrial mathematics Vol. 13; no. 3; pp. 405 - 417
Main Author:	Bykov, I. S.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-07-2019 Springer Nature B.V
Subjects:	Cubes Graph theory Hypercubes Mathematics Mathematics and Statistics n-dimensional hypercube factor perfect matching
Online Access:	Get full text
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Summary:	—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.
ISSN:	1990-4789 1990-4797
DOI:	10.1134/S1990478919030037