## Abstract

Let {T_{1},...,T_{k}} be a set of trees which is K_{h}-packable. It is shown that every n-vertex graph G=(V,E) with δ(G) ≥n/2+3h√n log n has k subgraphs S_{1},...,S_{k} with the following properties: 1. S_{i} is a set of [n/h] vertex-disjoint copies of T_{i}. 2. The subgraphs S_{1},...,S_{k} are edge-disjoint. 3. S_{1} ∪ ... ∪ S_{k} has maximum degree at most h -1. There are many interesting special cases of this result. To name just two: • If H is a tree with h vertices and G = (V,E) is a graph with n vertices, h divides n, and δ(G)≥n/2 + 3h√n log n, then G has an H-factor. • If h divides n, and δ(G)≥n/2 + 3h√n log n, then G has a set S of n star subgraphs, where for each i= 1,...,h, there are exactly n/h stars in S having i vertices, any two members of S having the same size are vertex-disjoint, and the union of all the members of S is an h - 1 regular spanning subgraph of G.

Original language | English |
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Pages (from-to) | 291-297 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 203 |

Issue number | 1-3 |

DOIs | |

State | Published - 28 May 1999 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics