论文信息 - On the Boundary of the Union of Planar Convex Sets

On the Boundary of the Union of Planar Convex Sets

Abstract. We give two alternative proofs leading to different generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n-12 arcs. (An arc is a connected piece of the boundary of one of the sets.) In the generalizations we allow pairs of boundaries to cross more than twice.

Micha Sharir | János Pach

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