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:本文旨在实现两个目标。首先,我们提出一个新的定向定理,通过将高阳等人的结果归约到Cs. Király关于有向图的对应定理,为高阳等人基于拟阵可达性的混合图中混合枝状树打包问题提供了一个自然且简洁的证明。其次,我们扩展了高阳等人的另一结果,提出了一个关于混合超图的新定理,该定理保证了混合超枝状树打包的存在性,使得其数量介于$\ell$和$\ell'$之间,每个顶点恰好属于其中$k个$,且每个顶点$v$作为根节点的次数介于$f(v)$和$g(v)$之间。