Hamiltonicity of hypercubes with a constraint of required and faulty edges

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

“…Let u and x be two distinct white vertices of Q n and v and y be two distinct black vertices of Q n . It is proved in [8] that there are two disjoint paths P 1 and P 2 such that (1) P 1 is a path joining u to v, (2) P 2 is a path joining x to y, and (3) P 1 ∪ P 2 spans Q n . We call such property the be the 2P property.…”

“…We call such property the be the 2P property. The 2P property has been used in many applications of hypercubes [8,12]. Obviously, the lengths of P 1 and P 2 satisfy l(P 1 ) + l(P 2 ) = 2 n − 2.…”

Edge-fault-tolerant diameter and bipanconnectivity of hypercubes

“…For (fault-tolerant) path and/or cycle embedding into hypercubes, see recent Refs. [2][3][4][5][6][7][8][9][10][11][13][14][15]17,[19][20][21][22] and a survey [23].…”