We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use this framework to establish an unconditional lower bound against the semidefinite programming + linear equations model, by showing that the relaxation does not solve the approximate graph homomorphism problem and thus, in particular, the approximate graph colouring problem.

翻译：我们提出了一种结合半定规划与线性丢番图方程的同态问题松弛方法，并基于结合方案的谱理论构建了一个分析其能力的框架。通过该框架，我们证明了该松弛方法无法解决近似图同态问题（进而特别地无法解决近似图着色问题），从而建立了针对半定规划+线性方程模型的无条件下界。