2026-07-22T21:00:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:609 2024-03-06T11:06:47Z ddc:004 open_access

Very Large Cliques are Easy to Detect Andreev, Alexander E. Jukna, Stasys Clique function monotone circuits perfect hashing It is known that, for every constant $kgeq 3$, the presence of a $k$-clique (a complete subgraph on $k$ vertices) in an $n$-vertex graph cannot be detected by a monotone boolean circuit using fewer than $Omega((n/log n)^k)$ gates. We show that, for every constant $k$, the presence of an $(n-k)$-clique in an $n$-vertex graph can be detected by a monotone circuit using only $O(n^2log n)$ gates. Moreover, if we allow unbounded fanin, then $O(log n)$ gates are enough. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Alexander E. Andreev and Stasys Jukna 2006 Is Part Of Dagstuhl Seminar Proceedings, Volume 6111, Complexity of Boolean Functions (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.06111.22 urn:nbn:de:0030-drops-6092 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06111.22 eng https://creativecommons.org/licenses/by/4.0/legalcode