A sharp lower bound on the independence number of k-regular connected hypergraphs with rank R

Let H(V, E) be a k-regular connected hypergraph with rank R on n vertices and m edges. A set of vertices \(S\subseteq V\) $S\subseteq V$ is an independent set if every two vertices in S are not adjacent. The independence number is the maximum cardinality of an independent set, denoted by \(\alpha (H)\) $\alpha (H)$ . In this paper, we prove the following inequality: \(\alpha (H)\ge \frac{m-(k-2)n-1}{R}\) $\alpha (H)\ge \frac{m-(k-2)n-1}{R}$ , and the equality holds if and only if H is a hypertree with R-perfect matching. Based on the proofs, some combinatorial algorithms on the independence number are designed.