### Abstract

Let K_{4}
^{3}-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n,K43-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree δ2(G)≥d contains ⌊n/4⌋ vertex-disjoint copies of K43-2e. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767-821) proved that t(n,K43-2e)=n4(1+o(1)) holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, A main ingredient in our proof is the recent "absorption technique" of Rödl, Ruciński, and Szemerédi (J. Combin. Theory Ser. A 116(3) (2009), 613-636).

Original language | English (US) |
---|---|

Pages (from-to) | 124-136 |

Number of pages | 13 |

Journal | Journal of Graph Theory |

Volume | 75 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2014 |

### Fingerprint

### Keywords

- absorbing
- factor
- hypergraphs
- tiling

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

_{4}

^{3}-2e.

*Journal of Graph Theory*,

*75*(2), 124-136. https://doi.org/10.1002/jgt.21726

**Tiling 3-uniform hypergraphs with K _{4}
^{3}-2e.** / Czygrinow, Andrzej; Debiasio, Louis; Nagle, Brendan.

Research output: Contribution to journal › Article

_{4}

^{3}-2e',

*Journal of Graph Theory*, vol. 75, no. 2, pp. 124-136. https://doi.org/10.1002/jgt.21726

_{4}

^{3}-2e. Journal of Graph Theory. 2014 Feb;75(2):124-136. https://doi.org/10.1002/jgt.21726

}

TY - JOUR

T1 - Tiling 3-uniform hypergraphs with K4 3-2e

AU - Czygrinow, Andrzej

AU - Debiasio, Louis

AU - Nagle, Brendan

PY - 2014/2

Y1 - 2014/2

N2 - Let K4 3-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n,K43-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree δ2(G)≥d contains ⌊n/4⌋ vertex-disjoint copies of K43-2e. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767-821) proved that t(n,K43-2e)=n4(1+o(1)) holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, A main ingredient in our proof is the recent "absorption technique" of Rödl, Ruciński, and Szemerédi (J. Combin. Theory Ser. A 116(3) (2009), 613-636).

AB - Let K4 3-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n,K43-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree δ2(G)≥d contains ⌊n/4⌋ vertex-disjoint copies of K43-2e. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767-821) proved that t(n,K43-2e)=n4(1+o(1)) holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, A main ingredient in our proof is the recent "absorption technique" of Rödl, Ruciński, and Szemerédi (J. Combin. Theory Ser. A 116(3) (2009), 613-636).

KW - absorbing

KW - factor

KW - hypergraphs

KW - tiling

UR - http://www.scopus.com/inward/record.url?scp=84889633131&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889633131&partnerID=8YFLogxK

U2 - 10.1002/jgt.21726

DO - 10.1002/jgt.21726

M3 - Article

AN - SCOPUS:84889633131

VL - 75

SP - 124

EP - 136

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 2

ER -