Spanning subdivisions in dense digraphs

Abstract

We prove that an $n$-vertex digraph $D$ with minimum semi-degree at least $\left(\frac{1}{2}+\varepsilon \right)n$ and $n\ge Cm$ contains a subdivision of all $m$-arc digraphs without isolated vertices. Here, $C$ is a constant only depending on $\varepsilon .$ This is the best possible and settles a conjecture raised by Pavez-Signé (2023) in a stronger form.