A digraph with minimum semidegree above ℓ/(2ℓ−1) times the tree size and with vertices of large out- and indegree contains every balanced antidirected bounded-degree tree of that size.
The regularity lemma and its applications in graph theory.Summer school on theoretical aspects of computer science, pages 84–112, 2000
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Antidirected trees in directed graphs
A digraph with minimum semidegree above ℓ/(2ℓ−1) times the tree size and with vertices of large out- and indegree contains every balanced antidirected bounded-degree tree of that size.