Thanks.
On Tuesday, June 9, 2015 at 1:50:51 PM UTC-5, Nathann Cohen wrote:
>
> > Didn't get you. Can you explain a bit more?
>
> A partition of the edges of a graph into disjoint matchings is called
> an edge-coloring. With the function I gave you, you can compute an
> edge-coloring of your graph which, because that graph is a K_{n,n},
> will be a collection of disjoint perfect matchings.
>
> Note that it may be a bit slow. You have a faster way to obtain what
> you desire with:
>
> sage: n=5;designs.transversal_design(2,n,resolvable=True)._classes
> [[[0, 5], [1, 6], [2, 7], [3, 8], [4, 9]],
> [[0, 6], [1, 7], [2, 8], [3, 9], [4, 5]],
> [[0, 7], [1, 8], [2, 9], [3, 5], [4, 6]],
> [[0, 8], [1, 9], [2, 5], [3, 6], [4, 7]],
> [[0, 9], [1, 5], [2, 6], [3, 7], [4, 8]]]
>
> What you see is a list of [list of pairs], and each [list of pairs] is
> a perfect matching in graphs.CompleteBipartiteGraph(n,n). They are all
> disjoint.
>
> Nathann
>
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