New sufficient degree conditions for an $r$-uniform hypergraph to be $k$-edge-connected

Abstract

An $r$-uniform hypergraphic sequence (i.e., $r$-graphic sequence) $d=(d_1,d_2,\cdots ,d_n)$ is said to be forcibly $k$-edge-connected if every realization of $d$ is $k$-edge-connected. In this paper, we obtain a strongest sufficient degree condition for $d$ to be $k$-edge-connected for all $k\ge 1$ and a strongest sufficient degree condition for $d$ to be super edge-connected. As a corollary, we give the minimum degree condition for $d$ to be maximally edge-connected. We also obtain another sufficient degree condition for $d$ to be $k$-edge-connected.