On the existence of a convex point subset containing one triangle in the plane

Let g ( k ) be the smallest integer such that every planar point set in general position with at least g ( k ) interior points has a convex subset with precisely k interior points. In this paper, we show that g ( 3 ) = 8 if the point sets have no empty convex hexagons.

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Bibliographic Details
Published in:Discrete mathematics 2005-12, Vol.305 (1), p.201-218
Main Author: Hosono, Kiyoshi
Format: Article
Language:English
Subjects:
Combinatorial convexity
Containment problem
Convex and discrete geometry
Exact sciences and technology
Geometry
Mathematics
Sciences and techniques of general use
The Erdős–Szekeres theorem
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Summary:Let g ( k ) be the smallest integer such that every planar point set in general position with at least g ( k ) interior points has a convex subset with precisely k interior points. In this paper, we show that g ( 3 ) = 8 if the point sets have no empty convex hexagons.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2005.07.006