The complexity of almost perfect matchings and other packing problems in uniform hypergraphs with high codegree

In addition, we use our reduction to show that a problem of deciding the existence of a perfect packing of the cycle C4(3) into a 3-uniform hypergraph H with minimum 2-wise vertex degree at least c|V(H)| is NP-complete only for c<14, which combined with a result from Kühn and Osthus (2006) [16] is, again, asymptotically tight.