Subgraphs, Closures and Hamiltonicity

摘要

Closure theorems in hamiltonian graph theory are of the following type: Let G bea 2-connected graph and let u, v be two distinct nonadjacent vertices of G. If condition c(u,v) holds, then G is hamiltonian if and only if G + uv is hamiltonian. The authors discuss several results of this type in which u and v are vertices of a subgraph H of G on 4 vertices and c(u,v) is a condition on the neighborhoods of the vertices of H (in G). The authors also discuss corresponding sufficient conditions for hamiltonicity of G.