# Exact minimum codegree threshold for K^{-}_{4}-factors

Research output: Contribution to journal › Article › peer-review

## Standard

**Exact minimum codegree threshold for K ^{-}_{4}-factors.** / Han, Jie; Lo, Allan; Treglown, Andrew; Zhao, Yi.

Research output: Contribution to journal › Article › peer-review

## Harvard

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_{4}-factors',

*Combinatorics, Probability and Computing*, vol. 26, pp. 856-885. https://doi.org/10.1017/S0963548317000268

## APA

^{-}

_{4}-factors.

*Combinatorics, Probability and Computing*,

*26*, 856-885. https://doi.org/10.1017/S0963548317000268

## Vancouver

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_{4}-factors. Combinatorics, Probability and Computing. 2017 Aug 4;26:856-885. https://doi.org/10.1017/S0963548317000268

## Author

## Bibtex

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## RIS

TY - JOUR

T1 - Exact minimum codegree threshold for K-4-factors

AU - Han, Jie

AU - Lo, Allan

AU - Treglown, Andrew

AU - Zhao, Yi

PY - 2017/8/4

Y1 - 2017/8/4

N2 - Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K − 4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K − 4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.

AB - Given hypergraphs F and H, an F-factor in H is a set of vertex-disjoint copies of F which cover all the vertices in H. Let K − 4 denote the 3-uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3-uniform hypergraph H on n vertices with minimum codegree at least n/2−1 contains a K − 4-factor. Our bound on the minimum codegree here is best possible. It resolves a conjecture of Lo and Markström [15] for large hypergraphs, who earlier proved an asymptotically exact version of this result. Our proof makes use of the absorbing method as well as a result of Keevash and Mycroft [11] concerning almost perfect matchings in hypergraphs.

KW - math.CO

KW - 05C35, 05C65, 05C70

KW - primary 05C70

KW - secondary 05C35

KW - 05C65

U2 - 10.1017/S0963548317000268

DO - 10.1017/S0963548317000268

M3 - Article

VL - 26

SP - 856

EP - 885

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

SN - 0963-5483

ER -