Matroid-reachability-based decomposition into arborescences
Combinatorics
2024-05-07 v1 Discrete Mathematics
Abstract
The problem of matroid-reachability-based packing of arborescences was solved by Kir\'aly. Here we solve the corresponding decomposition problem that turns out to be more complicated. The result is obtained from the solution of the more general problem of matroid-reachability-based -limited packing of arborescences where we are given a lower bound and an upper bound on the total number of arborescences in the packing. The problem is considered for branchings and in directed hypergraphs as well.
Cite
@article{arxiv.2405.03270,
title = {Matroid-reachability-based decomposition into arborescences},
author = {Florian Hörsch and Benjamin Peyrille and Zoltán Szigeti},
journal= {arXiv preprint arXiv:2405.03270},
year = {2024}
}