A new look at the concept of domination in hypergraphs

In this paper we propose a new definition of domination in hypergraphs in such a way that when restricted to graphs it is the usual domination in graphs. Let H = ( V,E ) be a hypergraph. A subset S of V is called a dominating set of H if for every vertex v in V - S, there exists an edge e ∈ E such that v ∈ e and e -{ v }⊆ S. The minimum cardinality of a dominating set of H is called the domination number of H and is denoted by γ ( H ) . We determine the domination number for several classes of uniform hypergraphs. We characterise minimal dominating sets and introduce the concept of independence and irredundance leading to domination chain in hypergraphs.