The edge‐connectivity of vertex‐transitive hypergraphs

Abstract

Abstract A graph or hypergraph is said to be vertex‐transitive if its automorphism group acts transitively upon its vertices. A classic theorem of Mader asserts that every connected vertex‐transitive graph is maximally edge‐connected. We generalise this result to hypergraphs and show that every connected linear uniform vertex‐transitive hypergraph is maximally edge‐connected. We also show that if we relax either the linear or uniform conditions in this generalisation, then we can construct examples of vertex‐transitive hypergraphs which are not maximally edge‐connected.