### 抄録

In this paper, we propose a new closure concept for spanning k-trees. A k-tree is a tree with maximum degree at most k. We prove that: Let G be a connected graph and let u and v be nonadjacent vertices of G. Suppose that (Formula presented) for every independent set S in G of order k with u, v ∈ S. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. This result implies Win's result (Abh Math Sem Univ Hamburg, 43:263-267, 1975) and Kano and Kishimoto's result (Graph Comb, 2013) as corollaries.

元の言語 | English |
---|---|

ページ（範囲） | 957-962 |

ページ数 | 6 |

ジャーナル | Graphs and Combinatorics |

巻 | 30 |

発行部数 | 4 |

DOI | |

出版物ステータス | Published - 2014 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### これを引用

*Graphs and Combinatorics*,

*30*(4), 957-962. https://doi.org/10.1007/s00373-013-1314-z

**Closure and Spanning k-Trees.** / Matsubara, Ryota; Tsugaki, Masao; Yamashita, Tomoki.

研究成果: Article

*Graphs and Combinatorics*, 巻. 30, 番号 4, pp. 957-962. https://doi.org/10.1007/s00373-013-1314-z

}

TY - JOUR

T1 - Closure and Spanning k-Trees

AU - Matsubara, Ryota

AU - Tsugaki, Masao

AU - Yamashita, Tomoki

PY - 2014

Y1 - 2014

N2 - In this paper, we propose a new closure concept for spanning k-trees. A k-tree is a tree with maximum degree at most k. We prove that: Let G be a connected graph and let u and v be nonadjacent vertices of G. Suppose that (Formula presented) for every independent set S in G of order k with u, v ∈ S. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. This result implies Win's result (Abh Math Sem Univ Hamburg, 43:263-267, 1975) and Kano and Kishimoto's result (Graph Comb, 2013) as corollaries.

AB - In this paper, we propose a new closure concept for spanning k-trees. A k-tree is a tree with maximum degree at most k. We prove that: Let G be a connected graph and let u and v be nonadjacent vertices of G. Suppose that (Formula presented) for every independent set S in G of order k with u, v ∈ S. Then G has a spanning k-tree if and only if G + uv has a spanning k-tree. This result implies Win's result (Abh Math Sem Univ Hamburg, 43:263-267, 1975) and Kano and Kishimoto's result (Graph Comb, 2013) as corollaries.

KW - Closure

KW - k-tree

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=84903200626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903200626&partnerID=8YFLogxK

U2 - 10.1007/s00373-013-1314-z

DO - 10.1007/s00373-013-1314-z

M3 - Article

AN - SCOPUS:84903200626

VL - 30

SP - 957

EP - 962

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 4

ER -