Asymptotic extremal construction for resilient k-graphs

Determine whether, for every fixed k ≥ 4 and all sufficiently large s depending on k, the maximum number m(k,s) of edges in a (k−1)-resilient k-uniform hypergraph with matching number s equals \binom{ks+k−1}{k}.

Background

The paper’s main general estimate concerns m(3,s), but the authors explain that the gap between their upper bound and the conjectured extremal scale remains large. They observe that the complete k-graph on ks+k−1 vertices is a natural construction and that, although it is not optimal for small s, they have found no better construction when k is fixed and s tends to infinity.

This observation motivates the stated asymptotic conjecture for fixed k ≥ 4 and sufficiently large s.