Geodesic
$2$-Factors without close edges in~the~$n$-dimensional cube
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 5-26

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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.
Mots-clés : $n$-dimensional hypercube
Keywords: perfect matching, $2$-factor. 
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     author = {I. S. Bykov},
     title = {$2${-Factors} without close edges in~the~$n$-dimensional cube},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {5--26},
     publisher = {mathdoc},
     volume = {26},
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     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_3_a0/}
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I. S. Bykov. $2$-Factors without close edges in~the~$n$-dimensional cube. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 3, pp. 5-26. http://geodesic.mathdoc.fr/item/DA_2019_26_3_a0/