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Pré-Publication, Document De Travail Année : 2023

Directed hypergraph connectivity augmentation by hyperarc reorientations

Résumé

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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Dates et versions

hal-04215599 , version 1 (22-09-2023)

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Moritz Mühlenthaler, Benjamin Peyrille, Zoltán Szigeti. Directed hypergraph connectivity augmentation by hyperarc reorientations. 2023. ⟨hal-04215599⟩
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