Name
Abstract | ||
|---|---|---|
According to the Erdős–Szekeres theorem, for every , a sufficiently large set of points in general position in the plane contains in convex position. In this note we investigate the line version of this result, that is, we want to find lines in convex position in a sufficiently large set of lines that are in general position. We prove almost matching upper and lower bounds for the minimum size of the set of lines in general position that always contains in convex position. This is quite unexpected, since in the case of points, the best known bounds are very far from each other. We also establish the dual versions of many variants and generalizations of the Erdős–Szekeres theorem. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00454-015-9705-y | Discrete & Computational Geometry |
Keywords | DocType | Volume |
Erdős–Szekeres theorem,Line arrangements,Duality,Convex position,Primary 52C10,52A37 | Journal | 54 |
Issue | ISSN | Citations |
3 | 0179-5376 | 0 |
PageRank | References | Authors |
0.34 | 14 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Imre Bárány | 1 | 435 | 95.10 |
| Edgardo Roldán-Pensado | 2 | 4 | 5.06 |
| Géza Tóth | 3 | 581 | 55.60 |