[seqfan] Re: partition of a circle
Ed Jeffery
lejeffery7 at gmail.com
Fri May 11 18:06:30 CEST 2012
In E^2, a Jordan domain is just a homeomorphic image of a closed disk: the
region must be connected and simply-connected (no holes), and it probably
has to be bounded as well. I believe that this is essentially the same
definition as that given for a "topological disk" from the theory of tiles
by Banko Grubaum, et al., in the volume "Tilings and Patterns" from 1987
which I no longer have in my library.
Ed
> Maybe one should also include the rule:
> There has to be at least one line segment (edge) connecting each
> internal node Q to a boundary node P. This would exclude Andrews n=3
> and n=5 graphs, and also Andrew's n=5 graph with all of the four
> 'outer' Qs connected to some Ps (now n=8), but the 'central' node Q is
> not connected to any P. Such a central Q is never connectable to any P
> (planarity).
> I have written yesterday to one of the authors (T. Zamfirescu at
> Dortmund TH) my zeroth order guess of the rules, and asked him for a
> definition of 'Jordan domain' on a euclidean plane E_2 (maybe some fans
> can here help also). I am waiting for his answer.
> Wolfdieter Lang
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