Exact minimum codegree threshold for K-4-factors

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

In: Combinatorics, Probability and Computing, Vol. 26, 04.08.2017, p. 856-885.

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@article{221369fc326f42689611088891137b7a,
title = "Exact minimum codegree threshold for K-4-factors",
abstract = "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 Markstr{\"o}m [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.",
keywords = "math.CO, 05C35, 05C65, 05C70, primary 05C70, secondary 05C35, 05C65",
author = "Jie Han and Allan Lo and Andrew Treglown and Yi Zhao",
year = "2017",
month = aug,
day = "4",
doi = "10.1017/S0963548317000268",
language = "English",
volume = "26",
pages = "856--885",
journal = "Combinatorics, Probability and Computing",
issn = "0963-5483",
publisher = "Cambridge University Press",

}

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 -