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：我们引入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，并提出了一个基于结合方案谱理论分析其能力的框架。通过该框架，我们证明了该松弛无法解决近似图同态问题（从而特别地无法解决近似图着色问题），进而建立了针对半定规划+线性方程模型的无条件下界。