### Abstract

For a graph H and an integer K ≥ 2, let σ _{k}(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ _{k+1} (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

Original language | English |
---|---|

Pages (from-to) | 137-154 |

Number of pages | 18 |

Journal | Ars Combinatoria |

Volume | 103 |

Publication status | Published - 2012 Jan |

### Keywords

- Claw-free graphs
- Degree sum
- Leaf
- Spanning tree

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Ars Combinatoria*,

*103*, 137-154.

**Spanning trees with a bounded number of leaves in a claw-free graph.** / Kano, Mikio; Kyaw, Aung; Matsuda, Haruhide; Ozeki, Kenta; Saito, Akira; Yamashita, Tomoki.

Research output: Contribution to journal › Article

*Ars Combinatoria*, vol. 103, pp. 137-154.

}

TY - JOUR

T1 - Spanning trees with a bounded number of leaves in a claw-free graph

AU - Kano, Mikio

AU - Kyaw, Aung

AU - Matsuda, Haruhide

AU - Ozeki, Kenta

AU - Saito, Akira

AU - Yamashita, Tomoki

PY - 2012/1

Y1 - 2012/1

N2 - For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

AB - For a graph H and an integer K ≥ 2, let σ k(H) denote the minimum degree sum of k independent Vertices of H. We prove that if a connected claw-free graph G satisfies σ k+1 (G) ≥ |G| -k, then G has a spanning tree with at most k leaves. We also show that the bound |G| -k is sharp and discuss the maximum degree of the required spanning trees.

KW - Claw-free graphs

KW - Degree sum

KW - Leaf

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=84855696786&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855696786&partnerID=8YFLogxK

M3 - Article

VL - 103

SP - 137

EP - 154

JO - Ars Combinatoria

JF - Ars Combinatoria

SN - 0381-7032

ER -