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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

Edmonds’ fundamental theorem on arborescences characterizes the existence of k 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 D=(V+x,A) be a digraph, P= {I1,,Il} be a partition of [k], c1,,cl,c1,,cl be nonnegative integers such that cαcα for α[l], F1,,Fk be k arc-disjoint x-arborescences in D such that iIαdFi+(x) cα for α[l]. We give a characterization on when F1,,Fk can be completed to arc-disjoint spanning x-arborescences F1,,Fk such that for any α[l], cαiIαdFi+(x) cα.



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 ķ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d=V+X一种 成为图, P= {一世1个一世} 成为...的一部分 [ķ]C1个CC1个C 是非负整数,使得 CαCα 对于 α[]F1个Fķķ 不相交的 X-树状 d 这样 一世一世αdF一世+X Cα 对于 α[]。我们对何时F1个Fķ 可以完成弧形不相交的跨越 X-树状 F1个Fķ 这样对于任何 α[]Cα一世一世αdF一世+X Cα

更新日期:2020-08-22
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