[seqfan] Re: eulerian orientations of hypercube graphs

Zach DeStefano zachdestefano at gmail.com
Fri Oct 28 19:05:08 CEST 2022


I found some bounds for this problem.

According to "Bounds on the Number of Eulerian Orientations" by A.
Schrijver (1983), the number of Eulerian orientations of a 2k-regular graph
on n vertices is between (2^-k (2k choose k))^n and sqrt((2k choose k)^n).

>From this we have that the value for d = 6 is between 2.9 x 10^25 and 4.3 x
10^41 and the value for d = 8 is between 1.2 x 10^164 and 1.5 x 10^236.

- Zach

On Fri, Oct 28, 2022 at 12:51 PM Hans Havermann <gladhobo at bell.net> wrote:

> Is it only a coincidence that A054759(4) is also 2970?
>
> http://oeis.org/A054759
>
> > On Oct 28, 2022, at 10:27 AM, hv at crypt.org wrote:
> >
> > I can confirm d=4 gives 2970.
>
>
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>



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