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    • Clique is hard on average for regular resolution 

      Atserias, Albert; Bonacina, Ilario; Rezende, Susanna F. de; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander (Association for Computing Machinery (ACM), 2018)
      Conference report
      Open Access
      We prove that for k ≪4√n regular resolution requires length nΩ(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 ...