Approximate Graph Colouring and the Crystal with a Hollow Shadow
Computational Complexity
2025-08-21 v4 Discrete Mathematics
Combinatorics
Optimization and Control
Abstract
We show that approximate graph colouring is not solved by the lift-and-project hierarchy for the combination of linear programming and linear Diophantine equations. The proof is based on combinatorial tensor theory.
Keywords
Cite
@article{arxiv.2211.03168,
title = {Approximate Graph Colouring and the Crystal with a Hollow Shadow},
author = {Lorenzo Ciardo and Stanislav Živný},
journal= {arXiv preprint arXiv:2211.03168},
year = {2025}
}
Comments
Full version of a STOC'23 paper and a SODA'23 paper (arXiv:2210.08293). Generalises and subsumes results from Section 6 in arXiv:2203.02478