When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06111.22
URN: urn:nbn:de:0030-drops-6092
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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

BibTeX - Entry

  author =	{Andreev, Alexander E. and Jukna, Stasys},
  title =	{{Very Large Cliques are Easy to Detect}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-6092},
  doi =		{10.4230/DagSemProc.06111.22},
  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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