### Abstract

We prove a conjecture of Horak that can be thought of as an extension of classical results including Dirac's theorem on the existence of Hamiltonian cycles. Namely, we prove for 1 ≤ k ≤ n - 2 if G is a connected graph with A ⊂ V (G) such that d_{G} (v) ≥ k for all v ∈ A, then there exists a subtree T of G such that V (T) ⊃ A and d_{T} (v) ≤ ⌈ frac(n - 1, k) ⌉ for all v ∈ A.

Original language | English |
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Pages (from-to) | 2749-2754 |

Number of pages | 6 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 9 |

DOIs | |

State | Published - 6 May 2009 |

### Keywords

- Subtrees through specified vertices

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## Cite this

Cutler, J. (2009). Trees through specified vertices.

*Discrete Mathematics*,*309*(9), 2749-2754. https://doi.org/10.1016/j.disc.2008.06.032