论文标题
最大独立混合植物的包装
Packing of maximal independent mixed arborescences
论文作者
论文摘要
Király在[最大独立树木包装上，暹罗J.离散。数学。 30（4）（2016），2107-2114]解决了以下包装问题：给定digraph $ d =（v，a）$，一组$ s = \ s = \ {s_ {1}，\ ldots，s_ {K} $ t_ {1}，\ ldots，t_ {k} $，带有roots $π（s_ {1}），\ ldots，π（s_ {k}）$，因此，对于任何$ v \ in v $，s sele $ \ \ {s_ {i}：v \ in V $ in v $ in v $ in v $ in v $ interv $ and and and Intriond intery intery intery interiondry Intrional intery intry and and and andirention in Inderity intery intery resription and and Intery is iS}在本文中，我们给出了新的特征，用于在矩阵约束下包装最大独立的混合植物。这种新的特征被简化为查找超模块函数的形式，该函数应被基于基质的根系混合图的每个强组件的方向覆盖。我们的证明带有多项式时间算法。请注意，我们的新特征将基拉利的结果扩展到混合图，这回答了一个已经引起了一些注意力的问题。
Király in [On maximal independent arborescence packing, SIAM J. Discrete. Math. 30 (4) (2016), 2107-2114] solved the following packing problem: Given a digraph $D = (V, A)$, a matroid $M$ on a set $S = \{s_{1}, \ldots,s_{k} \}$ along with a map $π: S \rightarrow V$, find $k$ arc-disjoint maximal arborescences $T_{1}, \ldots ,T_{k}$ with roots $π(s_{1}), \ldots ,π(s_{k})$, such that, for any $v \in V$, the set $\{s_{i} : v \in V(T_{i})\}$ is independent and its rank reaches the theoretical maximum. In this paper, we give a new characterization for packing of maximal independent mixed arborescences under matroid constraints. This new characterization is simplified to the form of finding a supermodular function that should be covered by an orientation of each strong component of a matroid-based rooted mixed graph. Our proofs come along with a polynomial-time algorithm. Note that our new characterization extends Király's result to mixed graphs, this answers a question that has already attracted some attentions.
