### 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 |
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Pages (from-to) | 137-154 |

Number of pages | 18 |

Journal | Ars Combinatoria |

Volume | 103 |

Publication status | Published - 2012 Jan 1 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Kano, M., Kyaw, A., Matsuda, H., Ozeki, K., Saito, A., & Yamashita, T. (2012). Spanning trees with a bounded number of leaves in a claw-free graph.

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