Name
Abstract | ||
|---|---|---|
The Hadwiger–Debrunner number HDd(p,q) is the minimal size of a piercing set that can always be guaranteed for a family of compact convex sets in Rd that satisfies the (p,q) property. Hadwiger and Debrunner showed that HDd(p,q)≥p−q+1 for all q, and equality is attained for q>d−1dp+1. Almost tight upper bounds for HDd(p,q) for a ‘sufficiently large’ q were obtained recently using an enhancement of the celebrated Alon–Kleitman theorem, but no sharp upper bounds for a general q are known. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.comgeo.2018.02.001 | Computational Geometry |
Keywords | Field | DocType |
(p,q)-Theorem,Hadwiger–Debrunner number,Helly-type theorems,Upper bound theorem,Convexity | Discrete mathematics,Combinatorics,Upper and lower bounds,Regular polygon,Mathematics,Upper bound theorem | Journal |
Volume | ISSN | Citations |
72 | 0925-7721 | 0 |
PageRank | References | Authors |
0.34 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chaya Keller | 1 | 3 | 4.52 |
| Shakhar Smorodinsky | 2 | 422 | 43.47 |