Strongly hyper-hamiltonian-laceability of hypercubes

Suppose that G = (V₀ U V₁, E) is a bipartite graph with two partite sets V₀ and V₁ of equal size. Let x and y be two arbitrary distinct vertices and let w be another vertex different from x and y. G is said to be strongly hyper-Hamiltonian-laceable if G - w satisfies the following three properties. P1: There is a (|V₀| + |V ₁| - 2)-length path between x and y, where x and y are in the same partite set and w is In the other partite set; P2: There is a (|V₀| + |V₁| - 3)-length path between x and y, where z and y are in different partite sets and w is in any partite set; P3: There is a (|V ₀| + |V₁| - 4)-length path between x and y, where x, y, w are in the same partite set. Let F_e be the set of faulty edges of an n-dimensional hypercube Q_n. In this paper, we show that Q_n - F_e (the graph obtained by deleting all edges of F_e from Q_n) remains strongly hyper-Hamiltonian-laceable when |F_e| ≤ n - 3.