Abstract: For two nondecreasing sequences $d=\left(d_1, d_2, \cdots, d_n\right)$ and $d^{\prime}=\left(d_1^{\prime}, d_2^{\prime}, \cdots, d_n^{\prime}\right)$ of nonnegative integers, we say that $d^{\prime}$ majorizes $d$, denoted by $d^{\prime} \geqslant d$, if $d_i^{\prime} \geqslant d_i$ for $1 \leqslant i \leqslant n$. An $r$-uniform hypergraphic sequence $d=\left(d_1, d_2, \cdots, d_n\right)$ is forcibly $k$-connected if every $r$-uniform hypergraph with degree sequence $d$ is $k$-connected. In this paper, we give a sufficient condition for an $r$-uniform hypergraphic sequence to be forcibly $k$-connected and observe that if an $r$-uniform hypergraphic sequence $d$ satisfies the condition (which implies $d$ is forcibly $k$-connected); then, any $r$-uniform hypergraphic sequence $d^{\prime} \geqslant d$ also satisfies the condition. As a corollary, we obtain the condition of Bondy for forcibly $k$-connected graphic sequences.

Key words: r-Uniform hypergraph, k-Connected, Monotone increasing condition, Weakly optimal