Vertex cover in hypergraphs

In graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that set. It is an extension of the notion of vertex cover in a graph.^{: 466–470}

An equivalent term is a hitting set: given a collection of sets, a set which intersects all sets in the collection in at least one element is called a hitting set. The equivalence can be seen by mapping the sets in the collection onto hyperedges.

Another equivalent term, used more in a combinatorial context, is transversal. However, some definitions of transversal require that every hyperedge of the hypergraph contains precisely one vertex from the set.