Graph products and chromatic numbers

Abstract

The problem of computing the chromatic number of a graph is considered. No known approximation algorithm can guarantee a better than O(n/sup 0.4/) coloring on a three-chromatic graph with n vertices. Evidence is provided that it is inherently impossible to achieve a better than n/sup epsilon / ratio in polynomial time by showing that 'breaking the n/sup epsilon / barrier' will automatically lead to vastly better polynomial-time approximation algorithms that achieve ratios closer to log n.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>