Upper bounds for vertex cover further improved

Abstract

The problem instance of Vertex Cover consists of an undirected graph G = (V,E) and a positive integer k, the question is whether there exists a subset C⊆ V of vertices such that each edge in E has at least one of its endpoints in C with |C| ≤ k. We improve two recent worst case upper bounds for Vertex Cover. First, Balasubramanian et al. showed that Vertex Cover can be solved in time O(kn+1:32472kk2), where n is the number of vertices in G. Afterwards, Downey et al. improved this to O(kn+1:31951kk2). Bringing the exponential base significantly below 1:3, we present the new upper bound O(kn+1:29175kk2).