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Andreev, Alexander E. ; Jukna, Stasys

Very Large Cliques are Easy to Detect

06111.JuknaStasys.Paper.609.pdf (0.2 MB)


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.

BibTeX - Entry

  author =	{Alexander E. Andreev and Stasys Jukna},
  title =	{Very Large Cliques are Easy to Detect},
  booktitle =	{Complexity of Boolean Functions},
  year =	{2006},
  editor =	{Matthias Krause and Pavel Pudl{\'a}k and R{\"u}diger Reischuk and Dieter van Melkebeek},
  number =	{06111},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Clique function, monotone circuits, perfect hashing}

Keywords: Clique function, monotone circuits, perfect hashing
Collection: 06111 - Complexity of Boolean Functions
Issue Date: 2006
Date of publication: 20.11.2006

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