In graph theory, there are two related properties of a hypergraph that are called its "width".
Meshulam[2] characterized the widths of a hypergraph H in terms of the properties of D(H).
Since L(H) is the complement of D(H), the above characterization can be translated to L(H): The domination number of a graph G, denoted γ(G), is the smallest size of a vertex set that dominates all vertices of G. The width of a hypergraph equals the domination number or its line-graph: w(H) = γ(L(H)).
This is because the edges of E are the vertices of L(H): every subset of E that pins E in H corresponds to a vertex set in L(H) that dominates all L(H).
[4] The matching width of a hypergraph equals the independence domination number or its line-graph: mw(H) = iγ(L(H)).