Better approximations of non-Hamiltonian graphs Original Research Article

Although there have been a lot of efforts to seek nice characterization of non-Hamiltonian graphs, little progress has been made so far. An important progress was achieved by Chvátal [5, 6]who introduced the class of non-1-tough graphs (N1T) and the class of non-sub-2-factor graphs (NS2F). Both contain only non-Hamiltonian graphs and the conditions for membership can be checked in non-deterministic polynomial time. Also it is known thatN1T ⊂- NS2F. Chvátal posed an open question about the complexity of those classes, i.e., whether or not they are NP-complete [6].