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

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magidin@math.berkeley.edu

Posts: 11,135
Registered: 12/4/04
Re: 4 colors problem
Posted: Mar 4, 2014 3:33 PM
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On Tuesday, March 4, 2014 12:24:11 PM UTC-6, swtch...@gmail.com wrote:
> ABABABA
>
> BABABAB
>
> ABABABA
>
>
>
> This checkered coloring scheme would not work since same colors are used in the adjacent countries in this case.


You seem to not understand the assumptions of the 4-color map theorem. In particular, "adjacency" only exists when countries share a common border of positive length; a single point (e.g., the four state corner in the US) does not count as adjacency between diagonally opposed countries.

If you ignore the hypotheses, it is usually easy to come up with a "counterexample". For instance, it is easy to draw a map on a torus that requires more than 4 colors; it does not invalidate the 4-color map theorem, however, because that is a theorem about *planar* maps, in which countries are *connected* and point adjacencies do not count.

Next time, perhaps you should familiarize yourself with the actual theorem you want to discuss, instead of addressing a straw man.

--
Arturo Magidin


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
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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
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3/4/14
Read Re: 4 colors problem
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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
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3/5/14
Read Re: 4 colors problem
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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
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