### Abstract

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.

Original language | English |
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Pages (from-to) | 39-46 |

Number of pages | 8 |

Journal | Discrete applied mathematics |

Volume | 51 |

Issue number | 1-2 |

DOIs | |

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 |

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## Cite this

Broersma, H. J., & Schiermeyer, I. (1994). Subgraphs, Closures and Hamiltonicity.

*Discrete applied mathematics*,*51*(1-2), 39-46. https://doi.org/10.1016/0166-218X(94)90092-2