## Vertex cover might be hard to approximate to within $$2 - \varepsilon$$.(English)Zbl 1133.68061

Summary: Based on a conjecture regarding the power of unique 2-prover-1-round games presented in [S. Khot, “On the power of unique 2-prover 1-round games”, in: Proc. 34th ACM Symp. on Theory of Computing, STOC, May 2002, 767–775 (2002)], we show that vertex cover is hard to approximate within any constant factor better than 2. We actually show a stronger result, namely, based on the same conjecture, vertex cover on $$k$$-uniform hypergraphs is hard to approximate within any constant factor better than $$k$$.

### MSC:

 68R10 Graph theory (including graph drawing) in computer science 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 68W25 Approximation algorithms
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### References:

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