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It is known that every hypercube Q n is a bipartite graph. Assume that n 2 and F is a subset of edges with |F | n − 2. We prove that there exists a hamiltonian path in Q n − F between any two vertices of different partite sets. Moreover, there exists a path of length 2 n − 2 between any two vertices of the same partite set. Assume that n 3 and F is a subset(More)
—The classical problem of diagnosability is discussed widely and the diagnosability of many well-known networks have been explored. In this paper, we consider the diagnosability of a family of networks, called the Matching Composition Network (MCN); two components are connected by a perfect matching. The diagnosability of MCN under the comparison model is(More)
In this paper, we investigate the fault-tolerant capabilities of the k-ary n-cubes for even integer k with respect to the hamiltonian and hamiltonian-connected properties. The k-ary n-cube is a bipartite graph if and only if k is an even integer. Let F be a faulty set with nodes and/or links, and let k 3 be an odd integer. When |F | 2n − 2, we show that(More)
—Diagnosis is an essential subject for the reliability of a multiprocessor system. Under the comparison diagnosis model, Sengupta and Dahbura proposed a polynomial-time algorithm with time complexity OðN 5 Þ to identify all the faulty processors for a given syndrome in a system with N processors. In this paper, we present a novel idea on system diagnosis(More)
It is known that there may not exist any stable matching for a given instance of the stable roommates problem. A stable partition is a structure that generalizes the notion of a stable matching; Tan (1991) proved that every instance of the stable roommates problem contains at least one such structure. In this paper we propose a new algorithm for finding a(More)