63.61 CompleteSubgraphs

CompleteSubgraphs( gamma )
CompleteSubgraphs( gamma, k )
CompleteSubgraphs( gamma, k, alls )

This function returns a set K of complete subgraphs of gamma, which must be a simple graph. A complete subgraph is represented by its vertex set. If <k> > -1 then the elements of K each have size k, otherwise the elements of K represent maximal complete subgraphs of gamma. The default for k is -1, i.e. maximal complete subgraphs.

The optional boolean parameter alls controls how many complete subgraphs are returned. If alls is true (the default), then K will contain (perhaps properly) a set of gamma.group orbit-representatives of the size k (if <k> > -1) or maximal (if <k> < 0) complete subgraphs of gamma.

If alls is false then K will contain at most one element. In this case, if <k> < 0 then K will contain just one maximal complete subgraph, and if <k> > -1 then K will contain a complete subgraph of size k if and only if such a subgraph is contained in gamma.

    gap> gamma := JohnsonGraph(5,2);;
    gap> CompleteSubgraphs(gamma);
    [ [ 1, 2, 3, 4 ], [ 1, 2, 5 ] ]
    gap> CompleteSubgraphs(gamma,2,false);
    [ [ 1, 2 ] ] 

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