On the domination of hypergraphs by their edges Original Research Article

Given a hypergraph ℋ = (E1,...,Em) with vertex set V, let no be the number of different possibilities for covering V by an odd number of Eʹs and ne the number of different possibilities for covering V when selecting an even number of Eʹs. The quantity d(V,ℋ) = no − ne is known as the (reliability) domination of H and a combinatorial invariant of considerable practical relevance. The present paper addresses the problem to determine this domination. After reviewing the current theory in the area we present some new relationships for d(V,ℋ) with respect to dual and interval hypergraphs.