Perfect Packings in Quasirandom Hypergraphs II

Abstract

For each of the notions of hypergraph quasirandomness that have been studied, we identify a large class of hypergraphs F so that every quasirandom hypergraph H admits a perfect F-packing. An informal statement of a special case of our general result for 3-uniform hypergraphs is as follows. Fix an integer r >= 4 and 0<p<1. Suppose that H is an n-vertex triple system with r|n and the following two properties: * for every graph G with V(G)=V(H), at least p proportion of the triangles in G are also edges of H, * for every vertex x of H, the link graph of x is a quasirandom graph with density at least p. Then H has a perfect $K_r^{(3)}$-packing. Moreover, we show that neither hypotheses above can be weakened, so in this sense our result is tight. A similar conclusion for this special case can be proved by Keevash's hypergraph blowup lemma, with a slightly stronger hypothesis on H.