Packing mixed hyperarborescences

Abstract

The aim of this paper is twofold. We first provide a new orientation theorem which gives a natural and simple proof of a result of Gao and Yang (2021) on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Király (2016) on directed graphs. Moreover, we extend another result of Gao and Yang (2021) by providing a new theorem on mixed hypergraphs having a packing of mixed hyperarborescences such that their number is at least $\ell$ and at most ${\ell }^{\prime }$, each vertex belongs to exactly $k$ of them, and each vertex $v$ is the root of least $f\left(v\right)$ and at most $g\left(v\right)$ of them.