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Abstract
Given hypergraphs F and H, an Ffactor in H is a set of vertexdisjoint copies of F which cover all the vertices in H. Let K ^{−} _{4} denote the 3uniform hypergraph with four vertices and three edges. We show that for sufficiently large n ∈ 4ℕ, every 3uniform 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.
Original language  English 

Pages (fromto)  856885 
Journal  Combinatorics, Probability and Computing 
Volume  26 
DOIs  
Publication status  Published  4 Aug 2017 
Keywords
 math.CO
 05C35, 05C65, 05C70
 primary 05C70
 secondary 05C35
 05C65
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Dive into the research topics of 'Exact minimum codegree threshold for K^{}_{4}factors'. Together they form a unique fingerprint.Projects
 2 Finished

A graph theoretical approach for combinatorial designs
Engineering & Physical Science Research Council
1/11/16 → 31/10/18
Project: Research Councils

EPSRC Fellowship: Dr Andrew Treglown  Independence in groups, graphs and the integers
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils