Year: 2009
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Nitzan, Noa
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394640566