(no subject)

posted by [identity profile] ornithoptercat.livejournal.com at 10:31am on 05/06/2006
I can easily think of a situation in 3-space where you'd have four 3D shapes representing countries (or whatever) all touching one another. Or is the problem nonexistant in that there is no upper limit to the number of colors you can force it to require?
[parent entry] [link] [reply]
 

(no subject)

posted by [identity profile] benlehman.livejournal.com at 10:40am on 05/06/2006
Yeah, you can pretty easily imagine an infinite set of mutually adjacent three dimensional objects.

The generalized four color map would be: "What is the maximum size of a set of mutually adjacent n-dimensional objects in an n-dimensional space?"
[link] [parent] [reply]
 

(no subject)

posted by [identity profile] benlehman.livejournal.com at 10:45am on 05/06/2006
To elaborate on the last post, here's what such a set looks like:

Picture a stack of boxes. Stack as many as you like.

Now, nail a plank to the top box so long it stretches down to touch the bottom box (and thus, naturally, touchs all the other boxes.) Nail a plank to the next box such that it, too stretches to the bottom. Etc, etc.

Picture it with ten or so and you see how you can stack as many boxes as you like this way.

yrs--
--Ben
[link] [parent] [reply]

May

SunMonTueWedThuFriSat
  1
 
 2
 
 3
 
 4
 
 5
 
 6
 
7
 
 8
 
 9
 
 10
 
 11
 
 12
 
 13
 
14
1
 15
 
 16
 
 17
 
 18
 
 19
 
 20
 
21
 
 22
 
 23
 
 24
 
 25
 
 26
 
 27
 
28
 
 29
 
 30
 
 31