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Tiling 3-Uniform Hypergraphs With math formula



Let math formula denote the hypergraph consisting of two triples on four points. For an integer n, let math formula denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree math formula contains math formula vertex-disjoint copies of math formula. Kühn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767–821) proved that math formula holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4,

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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).