## Abstract

In this paper, we address the problem of packing large trees in G_{n,p.} In particular, we prove the following result. Suppose that T_{1}, . . . , T_{N} are n-vertex trees, each of which has maximum degree at most (np)^{1/6/}(log n)^{6}. Then with high probability, one can find edge-disjoint copies of all the T_{i} in the random graph Gn,p, provided that p ≥ (log n)36/n and N ≤(1 − ε)np/2 for a positive constant ⊂. Moreover, if each T_{i} has at most (1 − α)n vertices, for some positive α, then the same result holds under the much weaker assumptions that p ≥(log n)2/(cn) and Δ(Ti) ≤ cnp/ log n that depends only on α and ε. Our assumptions on maximum degrees of the trees are significantly weaker than those in all previously known approximate packing results.

Original language | English |
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Pages (from-to) | 653-677 |

Number of pages | 25 |

Journal | Journal of the London Mathematical Society |

Volume | 99 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2019 |

## Keywords

- 05C05 (primary)

## All Science Journal Classification (ASJC) codes

- Mathematics(all)