Oriented Trees in Digraphs without Oriented $4$-cycles

Maya Stein, Ana Trujillo-Negrete

Published 2024-11-20Version 1

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.