Set of hypergraph nodes to which every hyperedge is connected
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.[1]: 466–470 [2]
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.
^Lovász, László; Plummer, M. D. (1986), Matching Theory, Annals of Discrete Mathematics, vol. 29, North-Holland, ISBN 0-444-87916-1, MR 0859549
^Berge, Claude (1973). Graphs and Hypergraphs. Amsterdam: North-Holland.
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