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 $n \geq C m$ 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-Sign\'{e} in a stronger form.