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.