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clique (Definition)

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.



"clique" is owned by Mathprof. [ full author list (3) | owner history (2) ]
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See Also: independent set and independence number

Also defines:  clique number, maximum clique
Keywords:  subgraph, maximal complete subgraph
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Cross-references: graph, subgraph
There are 2 references to this entry.

This is version 10 of clique, born on 2002-03-04, modified 2006-09-29.
Object id is 2752, canonical name is Clique2.
Accessed 7043 times total.

Classification:
AMS MSC: 05C69 (Combinatorics :: Graph theory :: Dominating sets, independent sets, cliques)
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