Non-Convexity
| dc.creator | Nitzan, Noa | |
| dc.date | 2009-01-26 | |
| dc.date.accessioned | 2026-07-07T12:34:47Z | |
| dc.date.available | 2026-07-07T12:34:47Z | |
| dc.description | Suppose S is a planar set. Two points a,b in S 'see each other' via S if [a,b] is included in S . F. Valentine proved in 1957 that if S is closed, and if for every three points of S, at least two see each other via S, then S is a union of three convex sets. The pentagonal star shows that the number three is best possible. We discard the condition that S is closed and show that S is a union of (at most) six convex sets. The number six is best possible. | |
| dc.identifier | https://arxiv.org/abs/0901.4139 | |
| dc.identifier | http://arxiv.org/abs/0901.4139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217561 | |
| dc.subject | Combinatorics | |
| dc.title | Non-Convexity | |
| dc.type | text |