Super edge-connectivity of transitive hypergraphs

Abstract

The properties of fragments and superatoms, first arose in the work of Mader et al., have turned out to be powerful tools in the study of graph connectivity. We generalize the concept of an edge fragment and an edge superatom to hypergraphs and reveal that these generalizations share features with the common concepts. As applications of these properties, we investigate the super edge-connectivity of uniform linear vertex transitive hypergraphs, uniform linear $t$-Cayley hypergraphs and linear edge transitive hypergraphs, and derive the main result of Burgess et al. [J. Graph Theory, 105(2024)252–259] as a corollary.