A closed (n + 1)-convex set in R2 is a union of n6 convex sets

M. A. Perles*, S. Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

It is shown that if a closed set S in the plane is (n+1)-convex, then it has no more than n4 holes. As a consequence, it can be covered by≤n6 convex subsets. This is an improvement on the known bound of 2n·n3.

Original languageEnglish
Pages (from-to)305-312
Number of pages8
JournalIsrael Journal of Mathematics
Volume70
Issue number3
DOIs
StatePublished - Oct 1990

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