### Abstract

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k*-container if the set of the vertices of all the paths in C(u, v) contains all the vertices of G. A graph G is k*-connected if there exists a k*-container between any two distinct vertices. Therefore, a graph is 1*-connected (respectively, 2*-connected) if and only if it is hamiltonian connected (respectively, hamiltonian). In this paper, a classical theorem of Ore, providing sufficient conditional for a graph to be hamiltonian (respectively, hamiltonian connected), is generalized to k*-connected graphs. (c) 2007 Published by Elsevier B.V.

Original language | English |
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Pages (from-to) | 1330-1333 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 7 |

DOIs | |

State | Published - 6 Apr 2008 |

### Keywords

- Hamiltonian connected; Hamiltonian; Ore theorem; Menger theorem

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## Cite this

Lin, C-K., Huang, H-M., Tan, J-M., & Hsu, L-H. (2008). On spanning connected graphs.

*Discrete Mathematics*,*308*(7), 1330-1333. https://doi.org/10.1016/j.disc.2007.03.072