Minimal 2-connected non-hamiltonian claw-free graphs Original Research Article

We say a graph G is minimal with respect to a property Q if there exists no proper induced subgraph G′ of G with property Q. In this paper we characterize all minimal graphs with respect to the property ‘to be 2-connected, non-hamiltonian and claw-free’. Several sufficient forbidden subgraph conditions are obtained as corollaries.