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Sat 29 Oct, 2005 11:21 pm
Hi all! I'm trying to figure out, first of all, what the question is even talking about, and then, maybe give it a shot.
Here goes:
Show that the infinite square lattice has both one-way and two-way infinite paths passing exactly once through each vertex.
Any input will be more than appreciated. Thanks!
I don't know if this is what is required, but how about:
1) spiral:
(0,0), (1,0), (1,1), (0,1), (-1,1), (-1,0), (-1,-1), (0,-1), (1,-1), (2,-1), (2,0), ...
2) intertwined, connected spirals both starting at (0,0):
(0,0), (0,-1), (1,-1), (1,0), (1,1), (1,2), (0,2), (-1,2), (-2,2), (-2, 1), (-2, 0), ...
The other half is the same, but with opposite signs.
markr, thanks for the input. I'll verify this as soon as I can. Also, how can I find an Eulerian trial in the infinite square lattice? Thanks!
Still confused on how to find an Eulerian trail in the infinite square lattice. Please advise. Thanks!
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