A closed (n + 1)-convex set inR
2 is a union ofn
6 convex sets |
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| Authors: | M A Perles S Shelah |
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| Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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| Abstract: | It is shown that if a closed setS in the plane is (n+1)-convex, then it has no more thann
4 holes. As a consequence, it can be covered by≤n
6 convex subsets. This is an improvement on the known bound of 2
n
·n
3.
The author would like to thank the BSF for partially supporting this research. Publication no. 354. |
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| Keywords: | |
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