On Pseudo-Convex Partitions of a Planar Point Set

Details On Pseudo-Convex Partitions of a Planar Point Set On Pseudo-Convex Partitions of a Planar Point Set

2010-11-08

arxiv.org/abs/1011.1866v1

Mathematics

Combinatorics

11 pages, 11 figures

Scientific paper

Aichholzer et al. [{\it Graphs and Combinatorics}, Vol. 23, 481-507, 2007] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number $\psi(n)$ satisfies, ${3/4}\lfloor{n/4}\rfloor\leq \psi(n)\leq\lceil{n/4}\rceil$. In this paper we improve the upper bound on $\psi(n)$ to $\lceil{3n/13}\rceil$, thus answering a question posed by Aichholzer et al. in the same paper.

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