Connectivity of Cartesian Product of Hypergraphs

A connected hypergraph H is maximally edge (resp. vertex)-connected if the edge (resp. vertex)-connectivity attains its minimum degree. A hypergraph H is super edge (resp. vertex)-connected if every minimum edge (resp. vertex) cut isolates a vertex of H. In this paper, sufficient conditions for the Cartesian product of hypergraphs to be maximally edge-connected, super edge-connected, maximally vertex-connected, and super vertex-connected are presented. As a corollary, we deduce that the n-dimensional r-uniform cube-hypergraph Q(n, r) is both super edge-connected and super vertex-connected.