We prove that for k ≪ 4√ n regular resolution requires length n Ω( k ) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k -clique. This lower bound is optimal up to the multiplicative constant in the exponent and also implies unconditional n Ω( k ) lower bounds on running time for several state-of-the-art algorithms for finding maximum cliques in graphs.

中文翻译：

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Clique 很难平均解决常规分辨率

我们证明对于ķ≪ 4√n常规分辨率需要长度n Ω(ķ)to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain aķ-集团。这个下限是最优的，直到指数中的乘法常数，也意味着无条件n Ω(ķ)用于在图中找到最大团的几种最先进算法的运行时间下限。