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Journal Articles The Electronic Journal of Combinatorics Year : 2021

## Packing of Mixed Hyperarborescences with Flexible Roots via Matroid Intersection

Florian Hoersch
Zoltán Szigeti

#### Abstract

Given a mixed hypergraph $\mathcal{F}=(V,\mathcal{A}\cup \mathcal{E})$, a non-negative integer $k$ and functions $f,g:V\rightarrow \mathbb{Z}_{\geq 0}$, a packing of $k$ spanning mixed hyperarborescences of $\mathcal{F}$ is called $(k,f,g)$-flexible if every $v \in V$ is the root of at least $f(v)$ and at most $g(v)$ of the mixed hyperarborescences. We give a characterization of the mixed hypergraphs admitting such packings. This generalizes results of Frank and, more recently, Gao and Yang. Our approach is based on matroid intersection, generalizing a construction of Edmonds. We also obtain an algorithm for finding a minimum weight solution to the problem mentioned above.

#### Domains

Mathematics [math] Combinatorics [math.CO]

### Dates and versions

hal-03326074 , version 1 (25-08-2021)

### Identifiers

• HAL Id : hal-03326074 , version 1
• ARXIV :
• DOI :

### Cite

Florian Hoersch, Zoltán Szigeti. Packing of Mixed Hyperarborescences with Flexible Roots via Matroid Intersection. The Electronic Journal of Combinatorics, 2021, 28 (3), ⟨10.37236/10105⟩. ⟨hal-03326074⟩

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