### Abstract

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on t vertices and ε > 0, the random graph G_{n,p}, with n a multiple of t, with high probability contains a family of edge-disjoint T-factors covering all but an ε-fraction of its edges, as long as ε^{4}np ≫ log^{2} n. Assuming stronger divisibility conditions, the edge probability can be taken down to p >. A similar packing result is proved also for pseudo- random graphs, defined in terms of their degrees and co-degrees.

Original language | English |
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Journal | Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 2 |

Publication status | Published - 16 Apr 2014 |

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### Keywords

- Packing
- Pseudo-random graphs
- Random graphs
- Tree factors

### Cite this

*Electronic Journal of Combinatorics*,

*21*(2).