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Clique Is Hard on Average for Regular Resolution
[article]
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