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Topic: A topological problem
Replies: 6   Last Post: Mar 2, 2013 9:39 AM

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Hauke Reddmann

Posts: 545
Registered: 12/13/04
A topological problem
Posted: Feb 26, 2013 12:17 PM
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Warning, incoming lousy ASCII, change to fixed font :-)

o o o
| | |
| O |
\ /|\ /
X | X
/ \|/ \
| O |
| | |
o o o

The lines |/\ are tied to the unmovable nodes Oo.
(As you see, four lines come out of O and one out of o.)
X denotes a crossing, which is like a virtual crossing
from knot theory, i.e. you can move it ad lib and any
line over any other. Should they cross in the process,
well duh, then you have more crossings.)

Can you move the lines around such that no horizontal
line going through this graph cuts more than three
of these lines? I think no, but can you lend me a
formal proof?
Hauke Reddmann <:-EX8
Die Weltformel: IQ+dB=const.

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