On pseudo-convex partitions of a planar point set

Aichholzer et al. [O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, C.D. Tóth, Decompositions, partitions, and coverings with convex polygons and pseudo-triangles, Graphs and Combinatorics 23 (2007) 481–507] introduced the notion of pseudo-convex partitioning of planar point sets and proved that t...

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Bibliographic Details
Published in:Discrete mathematics Vol. 313; no. 21; pp. 2401 - 2408
Main Authors: Bhattacharya, Bhaswar B., Das, Sandip
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2013
Subjects:
Combinatorial analysis
Convex hull
Coverings
Discrete geometry
Empty convex polygons
Graphs
Mathematical analysis
Partition
Partitioning
Partitions
Polygons
Pseudo-triangles
Upper bounds
Discrete geometry
Partition
Convex hull
Empty convex polygons
Pseudo-triangles
ISSN:0012-365X, 1872-681X
Online Access:Get full text
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Summary:Aichholzer et al. [O. Aichholzer, C. Huemer, S. Kappes, B. Speckmann, C.D. Tóth, Decompositions, partitions, and coverings with convex polygons and pseudo-triangles, Graphs and Combinatorics 23 (2007) 481–507] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number ψ(n) satisfies 34⌊n4⌋≤ψ(n)≤⌈n4⌉. In this paper we prove that ψ(13)=3, which improves the upper bound on ψ(n) to ⌈3n13⌉, thus answering a question posed by Aichholzer et al. in the same paper.
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ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2013.07.007