Abstract
Given a bipartite graph G with bipartition (X,Y), let F⊂E(G) be a set of faulty edges and let L be a linear forest in G−F such that |F|+|E(L)|≤k. Let u∈X and v∈Y be any two vertices such that none of the paths in L has u or v as internal vertices or both of them as end vertices. G is said to be k-fault-tolerant-prescribed hamiltonian laceable if G−F admits a hamiltonian path between u and v passing through L. Balanced hypercubes are candidate interconnection networks of multiprocessor systems. In this paper, we prove that the n-dimensional balanced hypercube is (n−1)-fault-tolerant-prescribed hamiltonian laceable.
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