### Abstract

Let k ≥ 2 be an integer. We show that if G is a (k + 1)-connected graph and each pair of nonadjacent vertices in G has degree sum at least |G| + 1, then for each subset S of V(G) with |S| = k, G has a spanning tree such that S is the set of endvertices. This result generalizes Ore's theorem which guarantees the existence of a Hamilton path connecting any two vertices.

Original language | English |
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Pages (from-to) | 13-18 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 24 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2008 Feb 1 |

Externally published | Yes |

### Keywords

- Hamilton path
- Hamilton-connected
- Leaf-connected
- Spanning tree

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Egawa, Y., Matsuda, H., Yamashita, T., & Yoshimoto, K. (2008). On a spanning tree with specified leaves.

*Graphs and Combinatorics*,*24*(1), 13-18. https://doi.org/10.1007/s00373-007-0768-2