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EdgeIdeals :: cliqueNumber

cliqueNumber -- computes the clique number of a graph

Synopsis

Description

cliqueNumber returns the clique number of a graph, the size of the largest clique contained in the graph. This number is also related to the dimension of the clique complex of the graph.

i1 : R = QQ[a..d];
 
i2 : cliqueNumber completeGraph R

o2 = 4
 
i3 : G = graph({a*b,b*c,a*c,a*d})

o3 = Graph{edges => {{a, b}, {a, c}, {b, c}, {a, d}}}
           ring => R
           vertices => {a, b, c, d}

o3 : Graph
 
i4 : cliqueNumber G

o4 = 3
 
i5 : dim cliqueComplex G + 1 == cliqueNumber G

o5 = true

See also

Ways to use cliqueNumber :

For the programmer

The object cliqueNumber is a method function.