4 research outputs found
Spanning paths in hypercubes
Given a family of pairwise distinct vertices of the -dimensional hypercube such that the distance of and is odd and , there exists a family of paths such that and are the endvertices of and partitions . This holds for any with one exception in the case when . On the other hand, for any there exist pairs of vertices satisfying the above condition for which such a family of spanning paths does not exist. We suggest further generalization of this result and explore a relationship to the problem of hamiltonicity of hypercubes with faulty vertices