Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On semidefinite programming relaxations for graph coloring and vertex cover
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Partial Covering Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Approximation algorithms for partial covering problems
Journal of Algorithms
The Lovász Number of Random Graphs
Combinatorics, Probability and Computing
On a restricted cross-intersection problem
Journal of Combinatorial Theory Series A
On hard instances of approximate vertex cover
ACM Transactions on Algorithms (TALG)
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
Vertex cover resists SDPs tightened by local hypermetric inequalities
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
On the approximability of the vertex cover and related problems
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Integrality Gaps of $2-o(1)$ for Vertex Cover SDPs in the Lovász-Schrijver Hierarchy
SIAM Journal on Computing
A better approximation ratio for the vertex cover problem
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
An edge-reduction algorithm for the vertex cover problem
Operations Research Letters
Vertex cover in graphs with locally few colors
Information and Computation
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Let vc(G) denote the minimum size of a vertex cover of a graph G=(V,E). It is well known that one can approximate vc(G) to within a factor of 2 in polynomial time; and despite considerable investigation, no $(2 - \varepsilon)$-approximation algorithm has been found for any $\varepsilon 0$. Because of the many connections between the independence number $\alpha(G)$ and the Lovász theta function $\vartheta(G)$, and because vc(G) = |V| - \alpha(G)$, it is natural to ask how well |V| - \vartheta(G)$ approximates vc(G). It is not difficult to show that these quantities are within a factor of 2 of each other ($|V| - \vartheta(G)$ is never less than the value of the canonical linear programming relaxation of vc(G)); our main result is that vc(G) can be more than $(2 - \varepsilon)$ times $|V| - \vartheta(G)$ for any $\varepsilon 0$. We also investigate a stronger lower bound than $|V|- \vartheta(G)$ for vc(G).