Upper bounds for Vertex Cover further improved

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 subset of or equal to V of vertices such that each edge in E has at least one of its endpoints in C with \C\ less than or equal to 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 + 1.32472(k)k(2)), where n is the number of vertices in G. Afterwards, Downey et al. improved this to O(kn + 1.31951(k)k(2)). Bringing the exponential base significantly below 1.3, we present the new upper bound O(kn + 1.29175(k)k(2)).