Timeline for Expected degree of a vertex in a tetrahedralization?
Current License: CC BY-SA 2.5
6 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Jun 1, 2010 at 12:30 | comment | added | momeara | @Bacher, O'Rourke: Investigating the number of tetrahedralizations in $\mathbb{R}^3$ is actually where this question came up. Sharir, Sheffer and Welzl's argument relied on bounding the the average number of vertices with degree $3$ in each triangulation to be not less than than $\frac{n}{30}$. Conceptually this is possible because $3$ is quite close to the expected degree of any vertex and most of the density is concentrated around the mean. In $\mathbb{R}^3$, if the expected degree of any vertex is not too large then some form of Sharir, Sheffer and Welzl's argument may go though. | |
| Jun 1, 2010 at 12:27 | history | edited | momeara | CC BY-SA 2.5 |
Corrrected the expected degree in the example because I forgot to divide through by $n$
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| Jun 1, 2010 at 10:25 | comment | added | Joseph O'Rourke | @Roland Bacher: Concerning your parenthetical remark, $30^n$ has been proved by Sharir, Sheffer, and Welzl: arXiv:0911.3352v1 [cs.DM]. | |
| Jun 1, 2010 at 7:50 | comment | added | Roland Bacher | Is there anything known on the number of tetrahedrisations of a generic configuration of $n$ points in $\mathbb R^3$. (In $\mathbb R^2$, it is known that the number of triangulations of a generic configuration of $n$ points is bounded by $C^n$ for some constant $C$, I believe, $C$ slightly bigger than $60$ has been proven to work.) | |
| Jun 1, 2010 at 4:13 | history | asked | momeara | CC BY-SA 2.5 |