Partition into strokes

[Max Alekseyev]

On 8/22/07, koh <zbi74583 at boat.zero.ad.jp> wrote:

> >     Or, "Partition of a graph G into strokes S_i" must satisfy the following conditions.
> >
> >     o Union_{i} S_i = H
> >     o If not{i=j} -> S_i and S_j don't have the same edge
> >     o If not{i=j} -> S_i U S_j isn't a dipath
> >     o For all i S_i is a dipath
> >          Where H is a digraph on G

[...]

>          "Partition of a graph G into strokes" means "Partition of a digraph H on graph G into strokes".

But what is exactly "a digraph on graph" ?

>          See the four conditions.
>
>     2) n=3
>          o-o-o   names of vertices 1-2-3
>
>          Partitions into strokes :
>          1->2->3
>          3->2->1
>          1->2, 3->2
>          2->1, 2->3
>          So, a(3)=4

I'm confused. All listed partitions represent partitions of
*different* digraphs.
Say, the first partition is of the digraph ( 1 -> 2 -> 3 ) while the
last partition is of the digraph ( 1 <- 2 -> 3 ). Clearly, these
digraphs are different.
So, what is H in this case and what exactly the equality "Union_{i}
S_i = H" from your definition means?

Regards,
Max