[seqfan] Re: A conjecture concerning connected rooted strength 1Eulerian graphs with n nodes
Valery Liskovets
liskov at im.bas-net.by
Fri Mar 13 11:54:16 CET 2009
"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
>
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