Characterizing forbidden pairs for hamiltonian properties Original Research Article

In this paper we characterize those pairs of forbidden subgraphs sufficient to imply various hamiltonian type properties in graphs. In particular, we find all forbidden pairs sufficient, along with a minor connectivity condition, to imply a graph is traceable, hamiltonian, pancyclic, panconnected or cycle extendable. We also consider the case of hamiltonian-connected graphs and present a result concerning the pairs for such graphs.