On convex decompositions of a planar point set

Let P be a planar point set in general position. Neumann-Lara et al. showed that there is a convex decomposition of P with at most 10 n − 18 7 elements. In this paper, we improve this upper bound to ⌈ 7 5 ( n − 3 ) ⌉ + 1 .

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Bibliographic Details
Published in:Discrete mathematics 2009-04, Vol.309 (6), p.1714-1717
Main Author: Hosono, Kiyoshi
Format: Article
Language:English
Subjects:
Combinatorial convexity
Convex and discrete geometry
Convex hull of a point set
Decomposition problem
Exact sciences and technology
Geometry
Mathematics
Sciences and techniques of general use
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Summary:Let P be a planar point set in general position. Neumann-Lara et al. showed that there is a convex decomposition of P with at most 10 n − 18 7 elements. In this paper, we improve this upper bound to ⌈ 7 5 ( n − 3 ) ⌉ + 1 .
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2008.02.008