In the following figure, a maximal matching " M " is marked with red, and the vertex cover " C " is marked with blue.
32.
Bipartite maximum matchings can be approximated arbitrarily accurately in constant time by distributed algorithms; in contrast, approximating the minimum vertex cover of a bipartite graph requires at least logarithmic time.
33.
For both connected well-covered graphs and well-covered graphs without isolated vertices, there can be no " essential vertices ", vertices which belong to every minimum vertex cover.
34.
An independent set is a set of vertices no two of which are adjacent, and a vertex cover is a set of vertices that includes at least one endpoint of each edge in the graph.
35.
The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem.
36.
Additionally, every well-covered graph is a critical graph for vertex covering in the sense that, for every vertex, deleting from the graph produces a graph with a smaller minimum vertex cover.
37.
His major contributions include an algorithm for approximating the weight of the Euclidean minimum spanning tree in sublinear time, and finding a tight integrality gap for the vertex cover problem using the Frankl R�dl graphs.
38.
The complement of a vertex cover in any graph is an independent set, so a minimum vertex cover is complementary to a maximum independent set; finding maximum independent sets is another NP-complete problem.
39.
The complement of a vertex cover in any graph is an independent set, so a minimum vertex cover is complementary to a maximum independent set; finding maximum independent sets is another NP-complete problem.
40.
It can be constructed using a simple polynomial-time procedure; and a given weighted constraint satisfaction problem is reducible to the problem of computing the minimum weighted vertex cover for its associated constraint composite graph.
