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

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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.

Original languageEnglish
Pages (from-to)405-417
Number of pages13
JournalJournal of Applied and Industrial Mathematics
Issue number3
Publication statusPublished - 1 Jul 2019


  • 2-factor
  • n-dimensional hypercube
  • perfect matching


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