Basic Packing of Arborescences
Olivier Durand de Gevigney, Viet-Hang Nguyen, Zolt\'an Szigeti

TL;DR
This paper characterizes digraphs that can be packed with arborescences under matroid constraints, extending classical results and providing polynomial-time algorithms for minimum cost packings.
Contribution
It extends Edmonds' and Katoh-Tanigawa's results to directed graphs with matroid constraints, offering a complete characterization and efficient algorithms.
Findings
Characterization of digraphs with arborescence packings under matroid constraints
Complete description of the convex hull of incidence vectors of basic packings
Polynomial-time algorithm for minimum cost arborescence packings
Abstract
We provide the directed counterpart of a slight extension of Katoh and Tanigawa's result on rooted-tree decompositions with matroid constraints. Our result characterises digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds' result on packing of spanning arborescences and implies - using a general orientation result of Frank - the above result of Katoh and Tanigawa. We also give a complete description of the convex hull of the incidence vectors of the basic packings of arborescences and prove that the mimimum cost version of the problem can be solved in polynomial time.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Markov Chains and Monte Carlo Methods
