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# clique

A maximal complete subgraph of a graph is a *clique*, and the *clique number* $\omega(G)$ of a graph $G$ is the maximal order of a clique in $G$. Simply, $\omega(G)$ is the maximal order of a complete subgraph of $G$. Some authors however define a clique as any complete subgraph of $G$ and refer to the other definition as maximum clique.

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

Defines:

clique number, maximum clique

Keywords:

subgraph, maximal complete subgraph

Related:

IndependentSetAndIndependenceNumber

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C69*no label found*

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