Tiling multipartite hypergraphs in quasi-random hypergraphs

Given k≥2 and two k-graphs (k-uniform hypergraphs) F H, an F-factor in H is a set of vertex disjoint copies that together covers the H. Lenz Mubayi studied problems quasi-random with minimum degree Ω(nk−1). In particular, they constructed sequence 1/8-dense 3-graphs H(n) Ω(n2) codegree Ω(n) but no K2,2,2-factor. We prove if p>1/8 3-partite 3-graph f vertices, then for sufficiently large n, all p-dense order n f|n have F-factors. That is, 1/8 density threshold ensuring F-factors given condition Ω(n). Moreover, we show one can not replace by condition. fact, find any p∈(0,1) n≥n0, there exist having study optimal each addition, also k-partite stronger assumption