Editing Clique (graph theory) (section)

==Definitions==
A '''clique''', {{mvar|C}}, in an [[undirected graph]] {{math|1=''G'' = (''V'', ''E'')}} is a subset of the [[Vertex (graph theory)|vertices]], {{math|''C'' ⊆ ''V''}}, such that every two distinct vertices are adjacent. This is equivalent to the condition that the [[induced subgraph]] of {{mvar|G}} induced by {{mvar|C}} is a [[complete graph]]. In some cases, the term clique may also refer to the subgraph directly.

A '''maximal clique''' is a clique that cannot be extended by including one more adjacent vertex, that is, a clique which does not exist exclusively within the vertex set of a larger clique. Some authors define cliques in a way that requires them to be maximal, and use other terminology for complete subgraphs that are not maximal.

A '''maximum clique''' of a graph, {{mvar|G}}, is a clique, such that there is no clique with more vertices. Moreover, the '''clique number''' {{math|''ω''(''G'')}} of a graph {{mvar|G}} is the number of vertices in a maximum clique in {{mvar|G}}.

The '''[[intersection number (graph theory)|intersection number]]''' of {{mvar|G}} is the smallest number of cliques that together cover all edges of {{mvar|G}}.

The '''clique cover number''' of a graph {{mvar|G}} is the smallest number of cliques of {{mvar|G}} whose union covers the set of vertices {{mvar|V}} of the graph.

A '''maximum clique transversal''' of a graph is a subset of vertices with the property that each maximum clique of the graph contains at least one vertex in the subset.{{sfnp|Chang|Kloks|Lee|2001}}

The opposite of a clique is an '''[[independent set (graph theory)|independent set]]''', in the sense that every clique corresponds to an independent set in the [[complement graph]]. The [[clique cover]] problem concerns finding as few cliques as possible that include every vertex in the graph.

A related concept is a '''biclique''', a [[complete bipartite graph|complete bipartite subgraph]]. The [[bipartite dimension]] of a graph is the minimum number of bicliques needed to cover all the edges of the graph.