Timeline for Minimum dimension for sphere packing a graph in Euclidean space
Current License: CC BY-SA 3.0
5 events
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| Jan 20, 2012 at 11:37 | comment | added | Joseph O'Rourke | @Will: Excellent point re shrinking! It is not clear one can shrink intersecting spheres to produce tangent spheres. Many simultaneous constraints... | |
| Jan 20, 2012 at 11:31 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Clarified upper bound argument.; deleted 208 characters in body
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| Jan 20, 2012 at 3:04 | comment | added | Will Jagy | Thanks, Joseph. Although I think they must be close, I think there may be graphs with a certain sphericity, but the more difficult task of arranging the spheres to be perfectly tangent may require an increase of dimension by 1 or 2. That is, it is not clear to me that we can shrink radii and perturb centers to improve a given sphere-intersecting arrangement into a sphere-tangency arrangement. We probably can, I suppose, I am not seeing very clearly what continuity methods give us here. | |
| Jan 20, 2012 at 0:53 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
added 1 characters in body
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| Jan 20, 2012 at 0:48 | history | answered | Joseph O'Rourke | CC BY-SA 3.0 |