### 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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics

### Cite this

*Graphs and Combinatorics*,

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

**On a spanning tree with specified leaves.** / Egawa, Yoshimi; Matsuda, Haruhide; Yamashita, Tomoki; Yoshimoto, Kiyoshi.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 24, no. 1, pp. 13-18. https://doi.org/10.1007/s00373-007-0768-2

}

TY - JOUR

T1 - On a spanning tree with specified leaves

AU - Egawa, Yoshimi

AU - Matsuda, Haruhide

AU - Yamashita, Tomoki

AU - Yoshimoto, Kiyoshi

PY - 2008/2

Y1 - 2008/2

N2 - 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.

AB - 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.

KW - Hamilton path

KW - Hamilton-connected

KW - Leaf-connected

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=43049130371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049130371&partnerID=8YFLogxK

U2 - 10.1007/s00373-007-0768-2

DO - 10.1007/s00373-007-0768-2

M3 - Article

VL - 24

SP - 13

EP - 18

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 1

ER -