Abstract
The n-dimensional balanced hypercube BHn is one of candidate interconnection networks for multiprocessor systems, and it is a bipartite graph. Let F be a set of faulty links and L be a fault-free linear forest in BHn. For any two nodes u and v in different parts of BHn such that none of the paths in L has u or v as internal node or both of them as end nodes, we prove that BHn admits a fault-free hamiltonian path between u and v passing through L even if the total number of links in F and L is up to 2n−2. The upper bound on the number of links in F and L is optimal. This generalizes some known results.
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