# Better Inapproximability Results for MaxClique, Chromatic Number and Min-3Lin-Deletion

@inproceedings{Khot2006BetterIR, title={Better Inapproximability Results for MaxClique, Chromatic Number and Min-3Lin-Deletion}, author={Subhash Khot and Ashok Kumar Ponnuswami}, booktitle={ICALP}, year={2006} }

We prove an improved hardness of approximation result for two problems, namely, the problem of finding the size of the largest clique in a graph and the problem of finding the chromatic number of a graph. We show that for any constant γ> 0, there is no polynomial time algorithm that approximates these problems within factor $n/2^{(\log n)^{3/4+\gamma}}$ in an n vertex graph, assuming ${\rm NP} \nsubseteq {\rm BPTIME}(2^{(\log n)^{O(1)}})$. This improves the hardness factor of $n/2^{(\log n)^{1…

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