[seqfan] Re: A conjecture concerning connected rooted strength 1Eulerian graphs with n nodes

[Valery Liskovets]

"Eulerian" means here having no odd-valent vertices, not necessarily connected.

Valery

Nikos Apostolakis wrote:

> On Fri, Mar 13, 2009 at 11:02:55AM +0200, thus spake Valery Liskovets:
>
> [...]
>
> >
> > Btw, there is a simple bijective transformation of arbitrary n-graphs into
> > rooted Eulerian (n+1)-graphs: add an external root-vertex and connect it
> > with the odd-valent vertices.
> >
>
> But what if the graph is Eulerian to begin with?  Then this construction
> just adds one isolated vertex resulting in a disconnected and therefore
> not Eulerian graph.
>
> Nikos
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/