Tiling 3-Uniform Hypergraphs With K43-2e

Let K-4(3) - 2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n,K-4(3) - 2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree delta(2)(G) >= d contains [n/4] vertex-disjoint copies of K-4(3)-2e. Kuhn and Osthus (J Combin Theory, Ser B 96(6) (2006), 767-821) proved that t(n, K-4(3) - 2e) = n/4(1 + o(1)) holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, t(n, K-4(3) - 2e) = {n/4 when n/4 is odd, n/4 + 1 when n/4 is even. A main ingredient in our proof is the recent "absorption technique" of Rodl, Rucinski, and Szemeredi (J. Combin. Theory Ser. A 116(3) (2009), 613-636). (c) 2013 Wiley Periodicals, Inc. J. Graph Theory 75: 124- 136, 2014