Minimum k-hamiltonian graphs, II

We consider in this paper graphs which remain hamiltonian after the removal of k edges (k-edge hamiltonian) or k vertices (k-hamiltonian). These classes of graphs arise from reliability considerations in network design. In a previous paper, W. W. Wong and C. K. Wong presented families of minimum k-hamiltonian graphs and minimum k-edge hamiltonian graphs for k even. Here, we complete this study in the case where k is odd.