## Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring

Citations: | 58 - 8 self |

### BibTeX

@MISC{Khot_improvedinapproximability,

author = {Subhash Khot},

title = {Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring},

year = {}

}

### OpenURL

### Abstract

In this paper, we present improved inapproximability re-sults for three problems: the problem of finding the maximum clique size in a graph, the problem of finding the chro-matic number of a graph, and the problem of coloring a graph with a small chromatic number with a small numberof colors. H*astad's celebrated result [13] shows that the maximumclique size in a graph with n vertices is inapproximable inpolynomial time within a factor n1-ffl for arbitrarily smallconstant ffl> 0 unless NP=ZPP. In this paper, we aimat getting the best subconstant value of ffl in H*astad's re-sult. We prove that clique size is inapproximable within a factor n2(log n)1-fl (corresponding to ffl = 1(log n)fl) for some constant fl> 0 unless NP ` ZPTIME(2(log n) O(1)). This improves the previous best inapproximability factor of