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In graph theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph H = , 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:
Since E contains all matchings in E, for all H: w ≥ mw.
The width of a hypergraph is used in Hall-type theorems for hypergraphs.
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