Degree Sequence Conditions for Maximally Edge-Connected and Super Edge-Connected Hypergraphs

Let H be a connected hypergraph with minimum degree $$\delta$$ and edge-connectivity $$\lambda$$. The hypergraph H is maximally edge-connected if $$\lambda = \delta$$, and it is super edge-connected or super-$$\lambda$$, if every minimum edge-cut consists of edges incident with some vertex. There are several degree sequence conditions, for example, Goldsmith and White (Discrete Math 23: 31–36, 1978) and Bollobas (Discrete Math 28:321–323, 1979) etc. for maximally edge-connected graphs and super-$$\lambda$$ graphs. In this paper, we generalize these and some other degree sequence conditions to uniform hypergraphs.