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Topic: 4 colors problem
Replies: 86   Last Post: Mar 13, 2014 4:36 PM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: 4 colors problem
Posted: Mar 5, 2014 7:09 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <5b66e1d6-0777-4171-864b-dda23f4a3025@googlegroups.com>,
swtchwrds88@gmail.com wrote:

> "The 4-color theorem doesn't claim that every partial 4-coloring
> of a planar graph can be completed to a full 4-coloring."
>
> The unit pattern (in the previous post I called it the unit function, but
> meant "unit pattern") guarantees a full 4-coloring, so it's reliable.
>
> "The claim of the theorem is that of _all_ possible valid
> colorings, at least one of them uses at most 4 colors."
>
> The unit pattern guarantees to use no more than 4 colors.
>
> "Thus, to show that a given planar graph is a counterexample to
> the 4-color theorem, it's not sufficient to produce a partial
> 4-coloring which can't be completed to a full coloring."
>
> The unit pattern uses a partial 4-coloring which completes to a full coloring
> for any-sized map and for any number of countries.
>
> "You would have to show that _all_ possible valid colorings use
> more than 4 colors, not just the one that you think makes sense."
>
> What does this mean?
>
> With a=blue, b=green, c=red, d=yellow,
> Color the following map accordingly,
>
> c d a b
> a b c d
> c d a b
> a b c d
> c d a b
>
> which fulfills the promise of the 4 color theorem.
> Now, let's say the second and third countries on the third row unites,
> so they have to share the same color.
> Now we have,
>
> c d a b
> a b c d
> c d d b
> a b c d
> c d a b
>
> How would you color this to fulfill the 4 color theorem using any coloring
> order?


Assuming each coloring colors a rectangle, with the 'dd' in the center
being a single rectangle, the coloring are acceptable as they stand.

Note that it is allowable for two regions to share one or more isolated
points of common boundary, but not any interval of positive length as
common boundary
--




Date Subject Author
3/3/14
Read 4 colors problem
stumblin' in
3/3/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/3/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/3/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read there should be a noncomputer proof of 4CT, I agree
Brian Q. Hutchings
3/4/14
Read Re: 4 colors problem
g.resta@iit.cnr.it
3/4/14
Read Re: 4 colors problem
stumblin' in
3/4/14
Read Re: 4 colors problem
Port563
3/4/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
quasi
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
quasi
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read also, what is the spatial analog
Brian Q. Hutchings
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/5/14
Read Re: 4 colors problem
Virgil
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
stumblin' in
3/5/14
Read Re: 4 colors problem
Virgil
3/5/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
Virgil
3/6/14
Read Re: 4 colors problem
Virgil
3/6/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/6/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
ross.finlayson@gmail.com
3/7/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/7/14
Read Re: 4 colours problem
Robin Chapman
3/6/14
Read Re: 4 colors problem
stumblin' in
3/6/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
Peter Percival
3/6/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
Peter Percival
3/7/14
Read Re: 4 colors problem
stumblin' in
3/7/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
Peter Percival
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
magidin@math.berkeley.edu
3/9/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/9/14
Read Re: 4 colors problem
stumblin' in
3/9/14
Read Re: 4 colors problem
stumblin' in
3/11/14
Read Re: 4 colors problem
stumblin' in
3/11/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/13/14
Read Re: 4 colors problem
stumblin' in
3/13/14
Read Re: 4 colors problem
Brian Q. Hutchings
3/13/14
Read Re: 4 colors problem
stumblin' in

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