The problem of matroid-based packing of arborescences was introduced and solved in Durand de Gevigney et al. (SIAM J Discret Math 27(1):567-574) . Frank (In personal communication) reformulated the problem in an extended framework. We proved in Fortier et al. (J Graph Theory 93(2):230-252) that the problem of matroid-based packing of spanning arborescences is NP-complete in the extended framework. Here we show a characterization of the existence of a matroid-based packing of spanning arborescences in the original framework. This leads us to the introduction of a new problem on packing of arborescences with a new matroid constraint. We characterize mixed graphs having a matroid-rooted, k-regular, (f, g)-bounded packing of mixed arborescences, that is, a packing of mixed arborescences such that their roots form a basis in a given matroid, 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. We also characterize dypergraphs having a matroid-rooted, k-regular, (f, g)-bounded packing of hyperarborescences.

Durand de Gevigney 等人介绍并解决了基于拟阵的树状排列问题。 （SIAM J 离散数学 27(1):567-574）。弗兰克（在个人交流中）在扩展框架中重新阐述了该问题。我们在 Fortier 等人中证明了。 (J Graph Theory 93(2):230-252) 基于拟阵的跨越树状结构的打包问题在扩展框架中是 NP 完全的。在这里，我们展示了原始框架中基于拟阵的跨越树状结构的存在性的表征。这导致我们引入了一个新的问题，即用新的拟阵约束来包装树状结构。我们描述了具有拟阵根、 k正则、( f , g ) 有界混合树状堆积的混合图，即混合树状堆积，使得它们的根形成给定拟阵中的基，每个顶点属于其中恰好k 个，每个顶点v是其中至少f ( v ) 和最多g ( v ) 的根。我们还描述了具有拟阵根、 k正则、 ( f , g ) 边界的超树状排列的 dypergraphs 的特征。