Embedding hamiltonian paths in hypercubes with a required vertex in a fixed position

The spanning connectivity of folded hypercubes☆

“…Lemma 2.7 [14]. Let x and y be two vertices from different partite sets of Q n (n P 2) and z be a vertex of Q n that is not in {x, y}.…”

Many-to-many n-disjoint path covers in n-dimensional hypercubes

“…Indeed, a one-to-one 1-disjoint path cover of a network is just a Hamiltonian path between any two nodes. A large amount of work on Hamiltonian path embeddings in various networks appeared in the literature [1][2][3][4][5]. On the other hand, for an embedding of disjoint paths in a network, a cover implies that every node can participate in a pipeline computation.…”