New results on \(k\)-independence of hypergraphs (Q2689120)

Lately, a huge interest is shown by researchers in defining an extension for the concept of the independence number of graphs. The $k$-independence number of a graph $G$ is the greatest size of a $k$-independent set of $G$ and is denoted by $\alpha_k(G)$. When one takes $k=0$ it becomes a usual independence number of $G$. Stimulated by the probe on the $k$-independence number of graphs, graph theorists started thinking about the independence number of hypergraphs. The authors in this paper investigate the $k$-independent set of $s$-uniform hypergraphs. They give for an $s$-uniform hypergraph $H$ of order $n$, a lower bound of the $k$-independence number in terms of the maximum degree. Then they find a lower bound for the $k$-independence number depending on the average degree.