### Abstract

In this paper, we give a sufficient condition for a graph to have a degree bounded spanning tree. Let n ≥ 1, k ≥ 3, c ≥ 0 and G be an n-connected graph. Suppose that for every independent set ⊆ of cardinality n(k-1) + c + 2, there exists a vertex set ⊆ of cardinality k such that the degree sum of vertices in X is at least {pipe}V(G){pipe} - c -1. Then G has a spanning tree T with maximum degree at most k + [c/n] and ∑_{ν∈V(T)} max{d_{T} (ν) - k, 0} ≤ c.

Original language | English |
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Pages (from-to) | 695-720 |

Number of pages | 26 |

Journal | Graphs and Combinatorics |

Volume | 26 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 Sep 1 |

Externally published | Yes |

### Keywords

- Degree bounded tree
- Degree sum condition
- Independence number
- Spanning tree
- Total excess

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Fujisawa, J., Matsumura, H., & Yamashita, T. (2010). Degree Bounded Spanning Trees.

*Graphs and Combinatorics*,*26*(5), 695-720. https://doi.org/10.1007/s00373-010-0941-x