Edge-connectivity of permutation hypergraphs
Résumé
In this note we provide a generalization of a result of Goddard, Raines and Slater on edge-connectivity of permutation graphs for hypergraphs. A permutation hypergraph G' is obtained from a hypergraph G by taking two disjoint copies of G and by adding a perfect matching between them. The main tool in the proof of the graph result was the theorem on partition constrained splitting off preserving k-edge-connectivity due to Bang-Jensen, Gabow, Jordán and Szigeti. Recently, this splitting off theorem was extended for hypergraphs by Bernáth, Grappe and Szigeti. This extension made it possible to find a characterization of hypergraphs for which there exists a k-edge-connected permutation hypergraph.