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Packing branchings under cardinality constraints on their root sets
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-08-22 , DOI: 10.1016/j.ejc.2020.103212 Hui Gao , Daqing Yang
中文翻译:
在根集中受基数约束的情况下打包分支
更新日期:2020-08-22
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-08-22 , DOI: 10.1016/j.ejc.2020.103212 Hui Gao , Daqing Yang
Edmonds’ fundamental theorem on arborescences characterizes the existence of pairwise arc-disjoint spanning arborescences with prescribed root sets in a digraph. In this paper, we study the problem of packing branchings in digraphs under cardinality constraints on their root sets by arborescence augmentation. Let be a digraph, be a partition of , be nonnegative integers such that for , be arc-disjoint -arborescences in such that for . We give a characterization on when can be completed to arc-disjoint spanning -arborescences such that for any , .
中文翻译:
在根集中受基数约束的情况下打包分支
埃德蒙兹关于树状的基本定理表征了 有向图中的指定根集合的成对弧不相交跨越树状结构。在本文中,我们研究了通过树状扩充在基数上受基数约束的有向图上的分支堆积问题。让 成为图, 成为...的一部分 , 是非负整数,使得 对于 , 是 不相交的 -树状 这样 对于 。我们对何时 可以完成弧形不相交的跨越 -树状 这样对于任何 , 。