About: Width of a hypergraph

In graph theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph H = (V, E), we say that a set K of edges pins another set F of edges if every edge in F intersects some edge in K. Then: * The width of H, denoted w(H), is the smallest size of a subset of E that pins E. * The matching width of H, denoted mw(H), is the maximum, over all matchings M in H, of the minimum size of a subset of E that pins M. Since E contains all matchings in E, for all H: w(H) ≥ mw(H). The width of a hypergraph is used in Hall-type theorems for hypergraphs.