New NP-hardness results for 3-Coloring and 2-to-1 Label Cover

Abstract

We show that given a 3-colorable graph, it is NP-hard to find a 3-coloring with $(16/17 + \eps)$ of the edges bichromatic. In a related result, we show that given a satisfiable instance of the 2-to-1 Label Cover problem, it is NP-hard to find a $(23/24 + \eps)$-satisfying assignment.

Corrected typos. arXiv admin note: substantial text overlap with arXiv:1204.5666