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, Yang \cite{GY} on matroid-reachability-based packing of mixed arborescences in mixed graphs by reducing it to the corresponding theorem of Cs. Kir\'aly \cite{cskir} on directed graphs. Moreover, we extend another result of Gao, Yang \cite{GY2} 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 $\ell'$, each vertex belongs to exactly $k$ of them, and each vertex $v$ is the root of least $f(v)$ and at most $g(v)$ of them.
翻译:本文有两个目的。首先,我们提出一个新的定向定理,通过将其简化为Cs.Király关于有向图的相应定理,为Gao、Yang关于混合图中基于拟阵可达性的混合树状图打包结果提供了一个自然且简单的证明。此外,我们扩展了Gao、Yang的另一结果,提出了一个关于混合超图的新定理,该定理表明存在一组混合超树状图的打包,使得其数量至少为$\ell$且至多为$\ell'$,每个顶点恰好属于其中$k个$,且每个顶点$v$至少是其中$f(v)$个、至多是$g(v)$个的根。