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 GπGπ is obtained from a hypergraph GG by taking two disjoint copies of GG 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 kk-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 kk-edge-connected permutation hypergraph.