Approximate graph colouring and the hollow shadow - Zivny, S; Ciardo, L (Association for Computing Machinery, 2023)
We show that approximate graph colouring is not solved by constantly many levels of the liftand-project hierarchy for the combined basic linear programming and affine integer programming relaxation. The proof involves a construction of tensors whose fixed-dimensional projections are equal up to reflection and satisfy a sparsity condition, which may be of independent interest.