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arXiv · 2003.04062

Packing of maximal independent mixed arborescences

Hui Gao·Daqing Yang
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Abstract

Kir\'{a}ly 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 $\pi : S \rightarrow V$, find $k$ arc-disjoint maximal arborescences $T_{1}, \ldots ,T_{k}$ with roots $\pi(s_{1}), \ldots ,\pi(s_{k})$, 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 Kir\'{a}ly's result to mixed graphs, this answers a question that has already attracted some attentions.

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BibTeXRIS

Hui Gao, Daqing Yang. 2020-03-09. Packing of maximal independent mixed arborescences. https://doi.org/10.1016/j.dam.2020.11.009

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