Matching and domination numbers in r-uniform hypergraphs

A matching is a set of pairwise disjoint hyperedges of a hypergraph H. The matching number $\mathit{\nu }(H)$ of H is the maximum cardinality of a matching. A subset D of vertices of H is called a dominating set of H if for every vertex v not in D there exists $u\in D$ such that u and v are contained in a hyperedge of H. The minimum cardinality of a dominating set of H is called the domination number of H and is denoted by $\mathit{\gamma }(H)$ . In this paper we show that every r‐uniform hypergraph H satisfies the inequality $\mathit{\gamma }(H)\le (r‐1)\mathit{\nu }(H)$ and the bound is sharp.