English

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