Timeline for Diameter of m-fold cover
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2009 at 3:11 | comment | added | Anton Petrunin | It seems that on this way, the best you can get is $2(m-1)d$... | |
| Dec 5, 2009 at 22:42 | comment | added | Anton Petrunin | That is right --- it is sufficient to make it for graphs. In fact any metric space (in particular Riemannian manifold) can be approximated by a graph, say in Gromov--Hausdorff sense. | |
| Dec 5, 2009 at 22:21 | comment | added | Alon Amit | That's right, and I modified my post to reflect that. However, I guess the point is that whatever the correct ratio is for graphs (up to subdivision, as outlined) should be the correct ratio for manifolds, right? If we can actually find a graph of diameter $d$ (say, a bipartite one to avoid the odd-cycle-diameter issue), and a connected $m$ cover with diamater $\alpha$md for $\alpha>1$, does this not also mean that the manifold case cannot be better? | |
| Dec 5, 2009 at 22:18 | history | edited | Alon Amit | CC BY-SA 2.5 |
Pointed out a flaw in the graph argument.
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| Dec 5, 2009 at 21:05 | comment | added | Anton Petrunin | I guess that "floor" means your tree? Then it might be up to $2d$ in each floor --- not $d$... | |
| Dec 5, 2009 at 18:12 | history | answered | Alon Amit | CC BY-SA 2.5 |