Geodesic
More on Planar Point Subsets with a Specified Number of Interior Points
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 752-756

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $g(k)$ be the smallest integer such that every set $P$ of points in the plane with no three collinear points and with at least $g(k)$ interior points has a subset containing precisely $k$ interior point of $P$. We prove that $g(k)\ge3k$ for $k\ge3$, which improves the known result that $g(k)\ge3k-1$ for $k\ge3$.
Keywords: interior point of a finite planar set, convex hull, deficient point set. 
@article{MZM_2008_83_5_a10,
     author = {Wei Xiang Lin and Ding Ren},
     title = {More on {Planar} {Point} {Subsets} with a {Specified} {Number} of {Interior} {Points}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {752--756},
     publisher = {mathdoc},
     volume = {83},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a10/}
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Wei Xiang Lin; Ding Ren. More on Planar Point Subsets with a Specified Number of Interior Points. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 752-756. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a10/