Vertex covers and connected vertex covers in 3-connected graphs

Abstract

Discusses time complexity analysis of the minimum vertex cover and minimum connected vertex cover problems for 3-connected graphs. A vertex cover of a graph G=(V, E) is a subset N of V such that each element of E is incident upon some element of N, where V and E are the sets of vertices and of edges of G, respectively. A connected vertex cover of a graph G is a vertex cover of G such that the subgraph G(N) induced by N of G is connected. The minimum vertex cover problem (VCP) is the problem of finding a vertex cover of minimum cardinality, and the minimum connected vertex cover problem is similarly defined. >