If an n-vertex r-uniform hypergraph has high minimum degree and no large empty r-partite subhypergraph, it contains every n-vertex bounded-degree linear hypertree.
A generalization of Carath´ eodory’s theorem.Discrete Math., 40(2-3):141–152, 1982
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Ramsey--Dirac theory for bounded degree hypertrees
If an n-vertex r-uniform hypergraph has high minimum degree and no large empty r-partite subhypergraph, it contains every n-vertex bounded-degree linear hypertree.