Geodesic
On the Existence of a Point Subset with Three or Five Interior Points
Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 105-115

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An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer $k\ge1$, let $h(k)$ be the smallest integer such that every point set in the plane, no three collinear, with at least $h(k)$ interior points, has a subset with $k$ or $k+2$ interior points of $P$. We prove that $h(3)=8$.
Keywords: finite planar point set, interior point. 
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     author = {Xianglin Wei and Wenhua Lan and Ren Ding},
     title = {On the {Existence} of a {Point} {Subset} with {Three} or {Five} {Interior} {Points}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2010},
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Xianglin Wei; Wenhua Lan; Ren Ding. On the Existence of a Point Subset with Three or Five Interior Points. Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 105-115. http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a8/