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Fault-tolerant Hamiltonian laceability of hypercubes. (English) Zbl 1043.68081
Summary: It is known that every hypercube Q n is a bipartite graph. Assume that n2 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 n3 and F is a subset of edges with |F|<n-3. We prove that there exists a Hamiltonian path in Q n -v-F between any two vertices in the partite set without v· Furthermore, all bounds are tight.
MSC:
68R10Graph theory in connection with computer science (including graph drawing)
05C45Eulerian and Hamiltonian graphs
68M15Reliability, testing and fault tolerance computer systems