# clique

A maximal http://planetmath.org/node/1757complete subgraph of a graph is a clique, and the clique number $\omega(G)$ of a graph $G$ is the \PMlinkescapephrasemaximal order maximal order of a clique in $G$. Simply, $\omega(G)$ is the maximal order of a subgraph of $G$. Some authors however define a clique as any subgraph of $G$ and refer to the other definition as maximum clique.

Adapted with permission of the author from by Béla Bollobás, published by Springer-Verlag New York, Inc., 1998.

Title clique Clique 2013-03-22 12:30:53 2013-03-22 12:30:53 Mathprof (13753) Mathprof (13753) 13 Mathprof (13753) Definition msc 05C69 IndependentSetAndIndependenceNumber clique number maximum clique