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GraphTheory

 FindClique
 find clique in graph

 Calling Sequence FindClique(G,size)

Parameters

 G - graph size - (optional) integer or range; size of clique to find

Description

 • FindClique returns a list of vertices which comprise a clique in the graph G. The optional parameter size specifies a size for the clique. If size is omitted, FindClique behaves identically to MaximumClique and returns a maximum clique.
 • The strategy is a branch-and-bound backtracking algorithm using the greedy color bound (see Kreher and Stinson, 1999).
 • For a faster algorithm that usually, but not always, returns a large clique, see GreedyClique.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $G≔\mathrm{GraphComplement}\left(\mathrm{CompleteGraph}\left(3,4\right)\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 7 vertices and 9 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G\right)$
 > $\mathrm{FindClique}\left(G,3\right)$
 $\left[{2}{,}{1}{,}{3}\right]$ (2)
 > $\mathrm{FindClique}\left(G,4\right)$
 $\left[{4}{,}{5}{,}{6}{,}{7}\right]$ (3)

References

 D.L. Kreher and D.R. Stinson, Combinatorial Algorithms: Generation, Enumeration and Search, CRC Press, Boca Raton, Florida, 1998.

Compatibility

 • The GraphTheory[FindClique] command was introduced in Maple 2018.
 • For more information on Maple 2018 changes, see Updates in Maple 2018.