# Upper Bounds for Vertex Cover Further Improved

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## 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* + 1.32472^{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}).

## Keywords

Search Tree Vertex Cover Optimal Cover Marked Vertex Search Tree Algorithm
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