In the mathematical discipline of graph theory, a covering (or cover) of a graph is a set of vertices (or edges) such that each edge (vertex) of the graph touches (is incident with) at least one element of the set.
A vertex covering of a graph G is a set of vertices V such that each edge of G is incident with at least one vertex in V. The set V is said to cover the edges of G. A minimum vertex covering is a vertex covering of smallest possible size. The vertex covering number is the size of a minimum vertex covering.
Dually, an edge covering of a graph G is a set of edges E such that each vertex is incident with at least one edge in E, with comparable concepts of covering the vertices of G, minimum edge covering, and edge covering number ΩE(G).
The term covering more frequently refers to a vertex covering rather than an edge covering.