The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 1,412
Registered: 12/3/04
Re: A topological problem
Posted: Feb 26, 2013 3:03 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <>, <>

> 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?

Can you move a crossing past an o? If so, the thing is a planar
graph: just move the four corner o's, top to bottom and bottom to top.

o o o
o o o

That fulfils your condition about horizontal lines. But is there some
other restriction on moving the crossings?

Ken Pledger.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.