New NP-hardness results for 3-Coloring and 2-to-1 Label Cover
Per Austrin, Ryan O'Donnell, Li-Yang Tan, John Wright
TL;DR
This paper establishes new NP-hardness thresholds for approximate 3-coloring and 2-to-1 Label Cover problems, indicating these problems remain computationally difficult even with near-perfect solutions.
Contribution
It provides improved NP-hardness bounds for approximate 3-coloring and 2-to-1 Label Cover, advancing understanding of their computational complexity.
Findings
NP-hard to find a 3-coloring with over 94.12% edges bichromatic
NP-hard to find a solution satisfying over 95.83% of constraints
Strengthens the theoretical limits of approximation for these problems
Abstract
We show that given a 3-colorable graph, it is NP-hard to find a 3-coloring with 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 -satisfying assignment.
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Taxonomy
TopicsAdvanced Graph Theory Research · Optimization and Search Problems · Graph Labeling and Dimension Problems