Closure theorems in hamiltonian graph theory are of the following type: Let G be a 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. We discuss several results of this type in which u and v are vertices of a subgraph H of G on four vertices and c(u, v) is a condition on the neighborhoods of the vertices of H (in G). We also discuss corresponding sufficient conditions for hamiltonicity of G.
|Number of pages||8|
|Journal||Discrete applied mathematics|
|Publication status||Published - 1994|
|Event||2nd Twente Workshop on Graphs and Combinatorial Optimization 1991 - University of Twente, Enschede, Netherlands|
Duration: 22 May 1991 → 24 May 1991