We prove that if D is a digraph of maximum outdegree and indegree at least k, and minimum semidegree at least k/2 that contains no oriented 4-cycles, then D contains each oriented tree T with~k arcs. This can be slightly improved if T is either antidirected or an arborescence.
@article{arxiv.2411.13483,
title = {Oriented Trees in Digraphs without Oriented $4$-cycles},
author = {Maya Stein and Ana Trujillo-Negrete},
journal= {arXiv preprint arXiv:2411.13483},
year = {2024}
}