Construction of maximum cycles in faulty binary hypercubes

Abstract

Consideration was given to the following problem. In the binary hypercube, given is a Hamiltonian cycle with faulty edges, or vertices, or both. Needed is to construct a lengthmaximum cycle without faulty components of the hypercube. The cycles are defined by the ring sequences of the weights of the hypercube edges belonging to them. The discussion was based on the example of a binary 4-dimensional hypercube.

Path Coverings with Prescribed Ends in Faulty Hypercubes

“…In [17] Parkhomenko illustrates some techniques of constructing cycles without faulty edges or vertices in low dimensional hypercubes. His methods rely on a classification of Hamiltonian cycles for hypercubes of dimension 4 or less.…”