Clique is not solvable by monotone circuits of polynomial size

René Thiemann
Archive of Formal Proofs 2022.

AFP entry

Abstract

Given a graph G with n vertices and a number s, the decision problem Clique asks whether G contains a fully connected subgraph with s vertices. For this NP-complete problem there exists a non-trivial lower bound: no monotone circuit of a size that is polynomial in n can solve Clique. This entry provides an Isabelle/HOL formalization of a concrete lower bound (the bound is (n^1/7)n^1/8 for the fixed choice of s = n^1/4), following a proof by Gordeev.

BibTex

@article{Clique_and_Monotone_Circuits-AFP,
author = {René Thiemann},
title = {Clique is not solvable by monotone circuits of polynomial size},
journal = {Archive of Formal Proofs},
month = {May},
year = {2022},
note = {\url{https://isa-afp.org/entries/Clique_and_Monotone_Circuits.html},
Formal proof development},
ISSN = {2150-914x},
}