On arborescence packing augmentation in hypergraphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916507290697728 |
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| author | Hoppenot, Pierre Szigeti, Zoltán |
| author_facet | Hoppenot, Pierre Szigeti, Zoltán |
| contents | We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum number of arcs to be added to a digraph so that in the resulting digraph there exists some special kind of packing of arborescences? We answer this question for two problems: $h$-regular \textsf{M}-independent-rooted $(f,g)$-bounded $(α, β)$-limited packing of mixed hyperarborescences and $h$-regular $(\ell, \ell')$-bordered $(α, β)$-limited packing of $k$ hyperbranchings. We also solve the undirected counterpart of the latter, that is the augmentation problem for $h$-regular $(\ell, \ell')$-bordered $(α, β)$-limited packing of $k$ rooted hyperforests. Our results provide a common generalization of a great number of previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On arborescence packing augmentation in hypergraphs Hoppenot, Pierre Szigeti, Zoltán Combinatorics Discrete Mathematics We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum number of arcs to be added to a digraph so that in the resulting digraph there exists some special kind of packing of arborescences? We answer this question for two problems: $h$-regular \textsf{M}-independent-rooted $(f,g)$-bounded $(α, β)$-limited packing of mixed hyperarborescences and $h$-regular $(\ell, \ell')$-bordered $(α, β)$-limited packing of $k$ hyperbranchings. We also solve the undirected counterpart of the latter, that is the augmentation problem for $h$-regular $(\ell, \ell')$-bordered $(α, β)$-limited packing of $k$ rooted hyperforests. Our results provide a common generalization of a great number of previous results. |
| title | On arborescence packing augmentation in hypergraphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2412.03357 |