TY - JOUR

T1 - 2-Factors Without Close Edges in the n-Dimensional Cube

AU - Bykov, I. S.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - —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.

AB - —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.

KW - 2-factor

KW - n-dimensional hypercube

KW - perfect matching

UR - http://www.scopus.com/inward/record.url?scp=85071643831&partnerID=8YFLogxK

U2 - 10.1134/S1990478919030037

DO - 10.1134/S1990478919030037

M3 - Article

AN - SCOPUS:85071643831

VL - 13

SP - 405

EP - 417

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -