hitting set | vertex covering

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can also more simply be thought of as a set S of vertices of G such that every edge of G has at least one of member of S as an endpoint. The vertex set of a graph is therefore always a vertex cover. The smallest possible vertex cover for a given graph G is known as a minimum vertex cover, and its size is called the vertex cover number, denoted τ(G). Vertex covers, indicated with red coloring, are shown above for a number of graphs. In a complete k-partite graph, and vertex cover contains vertices from at least k - 1 stages.

clique | edge cover | hungarian maximum matching algorithm | independent set | maximum independent vertex set | minimum vertex cover | vertex cover number | vertex cover polynomial