SUBGRAPHS, CLOSURES AND HAMILTONICITY

Closure theorems in hamiltonian graph theory arc of the following type : Let G be a 2-connected graph and let u, v be two distinct nonadjacen t vertices of G. If condition c(u, v) holds, then G is hamiltonian if and only if G + uv is hamiltonian. We discuss several results of this type in which u and v are vertices of a subgraph H of G on four vertic es and c(u, v) is a condition on the neighborhoods of the vertices of H (in G). We also discuss corresponding sufficient conditions for hami ltonicity of G.