/*
this disappears when adding a Integer() cast

sage: n = 20
sage: k = 3
sage: g = DiGraph()
sage: g.add_edges( (Integer(i),Integer(Mod(i+j,n))) for i in range(n)
for j in range(1,k+1) )
sage: k == g.edge_connectivity()
True
*/

Nathann

On 25 July 2010 15:27, Nathann Cohen <nathann.co...@gmail.com> wrote:
> Hello everybody !!!
>
> I was trying to write the following doctest, and noticed something scary :
>
> We build a directed circulant graph on n vertices by linking the i th
> vertex to i+1, i+2, ... , i+k, thus ensuring our graph is k-connected.
> Then, by Edmond's theorem, we know this graph has `k` edge-disjoint
> spanning arborescences
>
> sage: n = 20
> sage: k = 3
> sage: g = DiGraph()
> sage: g.add_edges( (i,Mod(i+j,n)) for i in range(n) for j in range(1,k+1) )
> sage: k == g.edge_connectivity()
> False
>
> This should be k, but it is not. Not *that* bad. But it gets worse :
>
> sage: g.strongly_connected_components()
> [[0], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]]
>
> Two different "0" ? Then I thought it was because of the Mod, and
> maybe some zeroes where regular ones, while other were zeroes of
> Z/20Z.... But then :
>
> sage: g
> Digraph on 21 vertices
> sage: len(g.vertices())
> 20
> sage: g.vertices()
> [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
>
> That's were I got really scared :-D
>
> Robert ? Could you please tell me "oh yeah, I know where it comes
> from, that's just a typo" ? :-D
>
> Thankssssssssssss !!!
>
> Nathann
>

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