You can color any map using only four or less colors! I can't remember the name of the guy who proved this but its true. Can anyone prove me wrong?
I mean to say that the four colors allow no color to touch the same color on and edge (but the areas may share a vertex point).
Weeel, itss aboot tieme wee goo back too Canada, eeehy boyss.
Ah, the old favourites....
http://www.google.com/search?q=4+colour+map+problem
If you dance barefoot on the broken glass of undefined behaviour, you've got to expect the occasional cut.
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>>Can anyone prove me wrong?
LOL...pft, why would we prove you wrong, if you didn't come up with that.
BTW, in my data structures and discrete math class, our prof said he will give out an A for the course if anyone can prove the theroem wrong...
some entropy with that sink? entropysink.com
there are two cardinal sins from which all others spring: Impatience and Laziness. - franz kafka
I bet he would seeing as it would make your prof instantly famous. No one has proved or disproved the theorem for a map of more than 25 regions. The proof published by Appel-Haken is not accepted and will not be accepted for a couple reasons.Originally Posted by axon
1). Parts are done on computers and cannot be verified by hand.
2). No one has been able to check the rest of the proof in it's entirety.
Can anyone link to a site that says in the theorem the regions cannot touch at a point? I searched and didnt find anything about that.
If no one can I will continue to think I am the winner so I feel special.
>> Can anyone prove me wrong?
Given a satisfactory set of axioms, quite easily.
>>Can anyone prove me wrong?
Yes. Your are wrong because i am right. I cannot be wrong because i am right. There fore if im always right and you are not me, you are wrong and therefore i have proved you to be wrong.
try coloring this map with only 4 colors....
(yes the land formation is completely unrealistic, but still!)
Make the yellow and the green areas both be green, then make the uncolored area be yellow.
Or if you wanted to fill in every area:
What about a square divided into 4 equal parts(4 smaller squares) and completely surrounded by the same land.
As I said, you just gotta play around with the axioms a bit. Here is a representation of one which (I am fairly sure, correct me if I am wrong) cannot be colored with only four colors. Its been umm... compressed sorta because I have no artistic skill, and a planar 2D space probably would not work for this kind of graph anyway, but the dots are colorable regions, and the lines between them signify that they share an edge.
echo Glirk Dient and Zach L.
I'm assuming the theorem does not allow regions to lie entirely around other ones...If that's not the case then Glirk Dient is probably right. I've tried to represent Zach's here on top and Glirk's on bottom. Zach's doesn't seem to work because one of the colors (in this case, the green) would have to cross over another one. (The green could be light blue)
Edit: I accidentally didn't make the yellow area connect to the green on the top one, but it wouldn't make a difference
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Glirk Dient's won't work, because two areas are allowed to have the same color if they only touch at a point (the areas may share a vertex point).
In the top one for JaWiB, the light blue can be changed to dark green.
In the bottom one, I assume the light blue and the dark blue overlap by more than just a vertex. If so, the red one can be turned yellow (or the yellow can be turned red). If not, then it is like Glirk Dient's comment, and you only need three colors.
I don't see areas in Zach L.'s picture. How does it apply?
