Clique Is Hard on Average for Regular Resolution [article]

Albert Atserias, Ilario Bonacina, Susanna F. de Rezende, Massimo Lauria, Jakob Nordström, Alexander Razborov
2020 arXiv   pre-print
We prove that for k ≪√(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.
arXiv:2012.09476v1 fatcat:3agob6qnf5btnp6ccd5i4smwgq