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- W1193275511 abstract "Let P be a set of n points in general position in the plane. In 1996, Urabe considered a partition of P into subsets S 1 ∪ ⋯ ∪ S l such that each S i forms a hole (or an empty convex polygon) of P and these holes are mutually disjoint. Let f ( P ) be the minimum number of holes over all such partitions of P and F ( n ) = max { f ( P ) } over all sets P of n points. Then the current best bounds are given by ⌈ n + 1 4 ⌉ ≤ F ( n ) ≤ ⌈ 5 n 18 ⌉ . In this paper, we prove that F ( n ) ≤ ⌈ n 4 ⌉ + 1 ." @default.
- W1193275511 created "2016-06-24" @default.
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- W1193275511 date "2015-10-01" @default.
- W1193275511 modified "2023-09-27" @default.
- W1193275511 title "On the minimum number of mutually disjoint holes in planar point sets" @default.
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- W1193275511 doi "https://doi.org/10.1016/j.comgeo.2015.07.001" @default.
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