A Planar 3-Convex Set is Indeed a Union of Six Convex Sets

Autor:	Noa Nitzan, Micha A. Perles
Rok vydání:	2013
Předmět:	Discrete mathematics Combinatorics Planar Computational Theory and Mathematics Non-convexity Regular polygon Convex set Discrete Mathematics and Combinatorics Geometry and Topology Theoretical Computer Science Mathematics
Zdroj:	Discrete & Computational Geometry. 49:454-477
ISSN:	1432-0444 0179-5376
DOI:	10.1007/s00454-012-9484-7
Popis:	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 the best possible. We drop 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::831a3dd2be50b83c98c5291b04c6c593 https://doi.org/10.1007/s00454-012-9484-7 Zobrazit plný text záznamu Full text from SpringerLink