Abstract
Suppose that G = (V0 ∪ 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 1-vertex-Hamiltonian-laceable if G - w satisfies the following three properties: P1. There is a (|V0| + |V1| - 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 x and y are in different partite sets and w is in any partite set; P3. There is a (|V0| + |V1| - 4)-length path between x and y, where x, y, w are in the same partite set. Let Fe be the set of faulty edges of an n-dimensional hypercube Qn. In this paper, we show that Qn - Fe (the graph obtained by deleting all edges of Fe from Qn) remains 1-vertex-Hamiltonian-laceable when |Fe| ≤ n - 3.
Published Version
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