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Clique Problem

CLIQUE: Given graph G = (V, E), find largest subset \(V' \subseteq V\) such that \(\forall u, v \in V'\), \((u, v) \in E\).
I.e., V' forms a complete subgraph of G (usually want largest).

CLIQUE = \(\{\langle G, k \rangle: \exists V' \subseteq V\) of size \(\geq k\) and \(\forall u, v \in V'\), \((u, v) \in E\}\)



Example



\psfig{figure=figures/f27-6.ps}

The running time of the CLIQUE algorithm is \(\Omega(k^2 \left( \begin{array}{c} \mid V \mid \\ k \end{array} \right))\)

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