Matroid-rooted packing of arborescences

Zoltán Szigeti ()
Additional contact information
Zoltán Szigeti: University Grenoble Alpes, Grenoble INP, CNRS, Laboratory G-SCOP

Journal of Combinatorial Optimization, 2024, vol. 48, issue 3, No 4, 17 pages

Abstract: Abstract The problem of matroid-based packing of arborescences was introduced and solved in Durand de Gevigney et al. (SIAM J Discret Math 27(1):567-574) . Frank (In personal communication) reformulated the problem in an extended framework. We proved in Fortier et al. (J Graph Theory 93(2):230-252) that the problem of matroid-based packing of spanning arborescences is NP-complete in the extended framework. Here we show a characterization of the existence of a matroid-based packing of spanning arborescences in the original framework. This leads us to the introduction of a new problem on packing of arborescences with a new matroid constraint. We characterize mixed graphs having a matroid-rooted, k-regular, (f, g)-bounded packing of mixed arborescences, that is, a packing of mixed arborescences such that their roots form a basis in a given matroid, each vertex belongs to exactly k of them and each vertex v is the root of least f(v) and at most g(v) of them. We also characterize dypergraphs having a matroid-rooted, k-regular, (f, g)-bounded packing of hyperarborescences.

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-024-01219-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01219-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-024-01219-6

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().