Journal of Graph Theory · 1984 · 45 citations · 0 references
ComputingComputer ScienceMathematicsCombinatoricsFault-tolerant ComputingFault-tolerant SystemsDirected Acyclic GraphsGraph AlgorithmsGraph TheoryNetwork OptimizationNetwork ReliabilityAlgorithmic Graph TheoryDirected GraphsGraph Theory In NetworksHamiltonian GraphsNetwork Design Problems
Abstract We consider two new classes of graphs arising from reliability considerations in network design. We want to construct graphs with a minimum number of edges which remain Hamiltonian after k edges (or k vertices) have been removed. A simple construction is presented for the case when k is even. We show that it is minimum k ‐edge Hamiltonian. On the other hand, Chartrand and Kapoor previously proved that this class of graphs was also minimum k ‐vertex Hamiltonian. The case when k is large (odd or even) is also considered. Some results about directed graphs are also presented.