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

作者：Nitzan Noa^*; Perles Micha A

来源：Discrete & Computational Geometry, 2013, 49(3): 454-477.

DOI：10.1007/s00454-012-9484-7

• Non-convexity
• Visually independent
• Seeing subset
• Invisibility graph
• Valentine's Theorem (57 ')

Suppose S is a planar set. Two points in S see each other via S if 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.

• 出版日期2013-4