Name
Abstract | ||
|---|---|---|
We prove that a collection of compact convex sets of bounded diameters in R d that is unbounded in k independent directions has a k -flat transversal for k < d if and only if every d +1 of the sets have a k -transversal. This result generalizes a theorem of Hadwiger(–Danzer–Grünbaum–Klee) on line transversals for an unbounded family of compact convex sets. It is the first Helly-type theorem known for transversals of dimension between 1 and d −1. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0925-7721(01)00025-6 | Comput. Geom. |
Keywords | Field | DocType |
convex sets,geometric transversal theory,k -unbounded,higher-dimensional transversals,helly-type theorem,k -transversal,convex set | Discrete mathematics,Combinatorics,Helly's theorem,Radon's theorem,Convex hull,Krein–Milman theorem,Convex set,Subderivative,Convex analysis,Mathematics,Danskin's theorem | Journal |
Volume | Issue | ISSN |
21 | 3 | Computational Geometry: Theory and Applications |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boris Aronov | 1 | 1430 | 149.20 |
| Jacob E. Goodman | 2 | 277 | 136.42 |
| Richard Pollack | 3 | 912 | 203.75 |