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Math Forum » Discussions » sci.math.* » sci.math.independent

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

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William Elliot

Posts: 590
Registered: 1/8/12
Re: A topological problem
Posted: Feb 28, 2013 12:44 AM
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On Tue, 26 Feb 2013, fc3a501@uni-hamburg.de wrote:

> 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.

What's a Oo node.

> (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?

Yes, move the bottom O to the top and visa versa to get.

o-o-o
|
o-o-o

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