### 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 |
---|---|

Journal | Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 2 |

State | Published - 16 Apr 2014 |

### Fingerprint

### Keywords

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

### Cite this

*Electronic Journal of Combinatorics*,

*21*(2).

}

*Electronic Journal of Combinatorics*, vol. 21, no. 2.

**Packing tree factors in random and pseudo-random graphs.** / Bal, Deepak; Frieze, Alan; Krivelevich, Michael; Loh, Po Shen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Packing tree factors in random and pseudo-random graphs

AU - Bal, Deepak

AU - Frieze, Alan

AU - Krivelevich, Michael

AU - Loh, Po Shen

PY - 2014/4/16

Y1 - 2014/4/16

N2 - 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 Gn,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 ε4np ≫ log2 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.

AB - 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 Gn,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 ε4np ≫ log2 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.

KW - Packing

KW - Pseudo-random graphs

KW - Random graphs

KW - Tree factors

UR - http://www.scopus.com/inward/record.url?scp=84898963331&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84898963331

VL - 21

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2

ER -