Bounded-degree hypertree universality conjecture for Steiner triple systems

A Steiner triple system on $n$ vertices is a 3-uniform hypergraph in which every pair of vertices is contained in exactly one edge. A hypertree is a connected, simple 3-uniform hypergraph in which every two vertices are joined by a unique path; its maximum degree is the largest number of edges containing any one vertex. Bounded-degree hypertree universality conjecture. Let $d$ be a fixed constant. Then any Steiner triple system on $n$ vertices contains all hypertrees with maximum degree at most $d$ and $n-o(n)$ vertices. The paper presents this as a likely easier variant of the broader conjecture that every Steiner triple system contains all hypertrees with $n-o(n)$ vertices; neither claim is established there.