New Results on k-independence of Hypergraphs

Let $H=(V,E)$ be an $s$-uniform hypergraph of order $n$ and $k\geq 0$ integer. A $k$-independent set $S\subseteq H$ is a vertices such that the maximum degree in induced by $S$ at most $k$. Denoted $\alpha_k(H)$ cardinality $H$. In this paper, we first give lower bound Furthermore, prove $\alpha_k(H)\geq \frac{s(k+1)n}{2d+s(k+1)}$ where $d$ average $H$,