Edge-connectivity of permutation hypergraphs

In this note we provide a generalization of a result of Goddard et al. (2003) [4] on edge-connectivity of permutation graphs for hypergraphs. A permutation hypergraph G π 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 et al. (1999) [1]. Recently, this splitting off theorem was extended for hypergraphs by Bernáth et al. (accepted in Journal of Graph Theory) [2]. This extension made it possible to find a characterization of hypergraphs for which there exists a k -edge-connected permutation hypergraph.