Let K43-2e 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).
ASJC Scopus subject areas
- Geometry and Topology