A matching is a set of pairwise disjoint hyperedges of a hypergraph H. The matching number \(\nu (H)\) 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 \(\gamma (H)\). In this paper we show that every r-uniform hypergraph H satisfies the inequality \(\gamma (H)\le (r-1)\nu (H)\) and the bound is sharp.
['Liying Kang', 'Shan Li', 'Yanxia Dong', 'Erfang Shan']
Matching and domination numbers in r-uniform hypergraphs