Non-Convexity

dc.creatorNitzan, Noa
dc.date2009-01-26
dc.date.accessioned2026-07-07T12:34:47Z
dc.date.available2026-07-07T12:34:47Z
dc.descriptionSuppose 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.identifierhttps://arxiv.org/abs/0901.4139
dc.identifierhttp://arxiv.org/abs/0901.4139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217561
dc.subjectCombinatorics
dc.titleNon-Convexity
dc.typetext

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