Every Steiner Triple System Contains Almost Spanning d-Ary Hypertree - Arman, Andrii; Rödl, Vojtěch; Sales, Marcelo Tadeu (The Electronic Journal of Combinatorics, 2022)
In this paper we make a partial progress on the following conjecture: for every μ>0 and large enough n, every Steiner triple system S on at least (1+μ)n vertices contains every hypertree T on n vertices. We prove that the conjecture holds if T is a perfect d-ary hypertree.