On Tue, 26 Feb 2013, firstname.lastname@example.org 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.