# 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 |
---|---|

Canonical name | Clique |

Date of creation | 2013-03-22 12:30:53 |

Last modified on | 2013-03-22 12:30:53 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 13 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 05C69 |

Related topic | IndependentSetAndIndependenceNumber |

Defines | clique number |

Defines | maximum clique |