Improved Hardness of Approximating Chromatic Number

TL;DR

This paper establishes a stronger NP-hardness result for coloring K-colorable graphs, showing it is computationally infeasible to color such graphs with significantly fewer than exponential in K^{1/3} colors.

Contribution

It improves the known hardness bounds for approximating the chromatic number of K-colorable graphs, advancing the theoretical understanding of graph coloring complexity.

Findings

Proves NP-hardness of coloring with fewer than 2^{K^{1/3}} colors for large K

Improves previous hardness bounds from K versus K^{O(log K)}

Strengthens the theoretical limits of graph coloring approximation

Abstract

We prove that for sufficiently large K, it is NP-hard to color K-colorable graphs with less than 2^{K^{1/3}} colors. This improves the previous result of K versus K^{O(log K)} in Khot [14].