cliqueClique22002-03-04 01:08:412006-09-29 17:13:30Definitionclique numbermaximum cliquesubgraphmaximal complete subgraph\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}\PMlinkescapeword{maximal}A maximal \PMlinkid{complete}{1757} subgraph of a graph is a \emph{clique}, and the \emph{clique number} $\omega(G)$ of a graph $G$ is the \PMlinkescapephrase{maximal order} maximal order of a clique in $G$. Simply, $\omega(G)$ is the maximal order of a \PMlinkescapetext{complete} subgraph of $G$. Some authors however define a clique as any \PMlinkescapetext{complete} subgraph of $G$ and refer to the other definition as \textit{maximum clique}.
\footnotesize{Adapted with permission of the author from \emph{\PMlinkescapetext{Modern Graph Theory}} by B\'{e}la Bollob\'{a}s, published by Springer-Verlag New York, Inc., 1998.}