[seqfan] Re: Number of Euler graphs: A002854 or something else?
N. J. A. Sloane
njas at research.att.com
Thu Jan 28 17:59:58 CET 2010
Max, I think you have misunderstood the definition of Euler graph.
An Euler graph is a graph with every node having even degree.
I will add a comment to A002854 to clarify this.
References for this definition are
1. the "classic" paper which underlies A002854, namely
%D A002854 C. L. Mallows and N. J. A. Sloane, Two-graphs, switching classes and Euler graphs are equal in number, SIAM J. Appl. Math., 28 (1975), 876-880.
(did you look at it?)
and 2. the earlier references that it cites.
Your definition :
> Let us assume the conventional definition of Euler graphs:
> a graph is Euler if there exists an Euler cycle, i.e., a cycle that
> goes through every edge in the graph exactly once.
is not right.
As you say, one should be very careful before changing the classic sequences!
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