Timeline for Extensions of the Koebe–Andreev–Thurston theorem to sphere packing?
Current License: CC BY-SA 3.0
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| Jan 13, 2012 at 19:30 | comment | added | Will Jagy | @S. Carnahan Thanks, I asked Igor the same thing, or tried to, I don't see that his argument applies to any possible incomplete graph on $n$ vertices. I think he was just showing me the induction step in the answer in his book, which is about the complete graphs. | |
| Jan 13, 2012 at 7:34 | comment | added | S. Carnahan♦ | In $\mathb{R}^{n-1}$, you have enough room to suitably perturb the simplex by some small $\epsilon$ without changing the sizes of the discs. If I'm not mistaken, you may also surround such a formation of discs with a $n+1$st disc turned inside-out (i.e., you can get a valid formation by a Möbius transformation). | |
| Jan 13, 2012 at 6:21 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jan 13, 2012 at 6:09 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jan 13, 2012 at 3:48 | history | edited | Will Jagy | CC BY-SA 3.0 |
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| Jan 13, 2012 at 3:43 | history | answered | Will Jagy | CC BY-SA 3.0 |