Name
Abstract | ||
|---|---|---|
We show that a set of n disjoint unit spheres in Rd admits at most two distinct geometric permutations if n ≥ 9, and at most three if 3 ≤ n ≤ 8. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in R3: if any subset of size at most 18 of a family of such spheres admits a line transversal, then there is a line transversal for the entire family. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.comgeo.2004.08.003 | Comput. Geom. |
Keywords | Field | DocType |
n disjoint unit sphere,line transversals,hadwiger-type theorem,unit ball,entire family,geometric permutation,disjoint unit sphere,line transversal,helly-type theorem,unit sphere,distinct geometric permutation,computational geometry,discrete geometry,combinatorial geometry | Discrete geometry,Discrete mathematics,Combinatorics,Disjoint sets,Permutation,Computational geometry,Ball (bearing),Transversal (geometry),SPHERES,Mathematics,Unit sphere | Journal |
Volume | Issue | ISSN |
30 | 3 | Computational Geometry: Theory and Applications |
Citations | PageRank | References |
17 | 1.27 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Otfried Cheong | 1 | 594 | 60.27 |
| Xavier Goaoc | 2 | 138 | 20.76 |
| Hyeon-suk Na | 3 | 183 | 17.53 |