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arXiv · 2304.14868

Directed hypergraph connectivity augmentation by hyperarc reorientations

Moritz Mühlenthaler·Benjamin Peyrille·Zoltán Szigeti
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Abstract

The orientation theorem of Nash-Williams states that an undirected graph admits a $k$-arc-connected orientation if and only if it is $2k$-edge-connected. Recently, Ito et al. showed that any orientation of an undirected $2k$-edge-connected graph can be transformed into a $k$-arc-connected orientation by reorienting one arc at a time without decreasing the arc-connectivity at any step, thus providing an algorithmic proof of Nash-Williams' theorem. We generalize their result to hypergraphs and therefore provide an algorithmic proof of the characterization of hypergraphs with a $k$-hyperarc-connected orientation originally given by Frank et al. We prove that any orientation of an undirected $(k,k)$-partition-connected hypergraph can be transformed into a $k$-hyperarc-connected orientation by reorienting one hyperarc at a time without decreasing the hyperarc-connectivity in any step. Furthermore, we provide a simple combinatorial algorithm for computing such a transformation in polynomial time.

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Moritz Mühlenthaler, Benjamin Peyrille, Zoltán Szigeti. 2023-04-28. Directed hypergraph connectivity augmentation by hyperarc reorientations. https://arxiv.org/abs/2304.14868

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