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Dear GAP-Forum,

On Thu, Nov 20, 2003 at 09:40:57AM -0500, Drew Krause wrote:

> I would like to be able to do the following using GAP and the grape

> package. I need help in the proper way to formulate the problem in terms

> of the software:

>

> (1) Take the set of non-identical pairs (x,y) from a set of n elements.

> Two pairs would be connected if the intersection of its members was

> empty. For example. the pairs (1,3) and (4,2) would be connected, but

> (1,3) and (2,3) would not.

just do (after RequirePackage("grape")) the following:

ComplementGraph(JohnsonGraph(n,2));

>

> (2) Generalize the above to tuples of length greater than 2. For

> example, (1,3,4) and (2, 5, 6) would be connected since there is no

> intersection among the members.

for k being the size of the subsets:

g:=SymmetricGroup(n);; Graph(g,Orbit(g,[1..k],OnSets),OnSets, function(x,y) return Size(Intersection(x,y))=0; end, true);

HTH,

Dmitrii

Dmitrii Pasechnik

http://www.thi.informatik.uni-frankfurt.de/~dima/

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