Geodesic
Packing of mixed hyperarborescences with flexible roots via matroid intersection
Florian Hörsch1 ; Zoltán Szigeti1
1GSCOP, Grenoble
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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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.
DOI : 10.37236/10105
Classification : 05C70, 05C65, 05C40, 05C20, 05B35, 05C85
Mots-clés : mixed graphs, edge-disjoint spanning trees, arborescences

Florian Hörsch  1   ; Zoltán Szigeti  1

1 GSCOP, Grenoble 
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     title = {Packing of mixed hyperarborescences with flexible roots via matroid intersection},
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Florian Hörsch; Zoltán Szigeti. Packing of mixed hyperarborescences with flexible roots via matroid intersection. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10105

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