Vertex Cover Kernelization

Years and Authors of Summarized Original Work

• 2004; Abu-Khzam, Collins, Fellows, Langston, Suters, Symons

Problem Definition

Let G be an undirected graph. A subset C of vertices in G is a vertex cover for G if every edge in G has at least one end in C. The (parametrized) vertex cover problem is for each given instance (G, k), where G is a graph and ${ k \geq 0 }$ is an integer (the parameter), to determine whether the graph G has a vertex cover of at most k vertices.

The vertex cover problem is one of the six “basic” NP-complete problems according to Garey and Johnson [4]. Therefore, the problem cannot be solved in polynomial time unless P ${ = }$ NP. However, the NP-completeness of the problem does not obviate the need for solving it because of its fundamental importance and wide applications. One approach was initiated based on the observation that in many applications, the parameter kis small. Therefore, by taking the advantages of this fact, one may be able to solve this...