Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any fixed k 3, we estimate P k (n), the maximum size of a family F with the property that any k members of F are in convex position, but no n are. In particular, for k = 3, we improve the triply exponential upper bound of T. Bisztriczky and G. Fejes T'oth by showing that P 3 (n) ! 16 n . 1 Introduction In their classical paper [ES1], Erdos and Szekeres proved that any set of more than i 2n\Gamma4 n\Gamma2 j points in general position in the plane contains n points which are in convex position, i.e., they form the vertex set of a convex n-...
AbstractWe answer some questions of Tverberg about separability properties of families of convex set...
In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g...
According to the Erd˝os–Szekeres theorem, every set of n points in the plane contains roughly log n ...
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex posit...
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex posit...
A family F of convex sets is said to be in convex position, if none of its members is contained in...
Let g(n) denote the least integer such that among any g(n) points in general position in the plane t...
Let ES(n) denote the least integer such that among any ES(n) points in general position in the plane...
Let f(k; n), n k 3, denote the smallest positive integer such that any set of f(k; n) points, in ...
Abstract. According to the Erdős-Szekeres theorem, for every n, a suffi-ciently large set of points...
AbstractIn 1935 Pál Erdős and György Szekeres proved that, roughly speaking, any configuration of n ...
The Erdős-Szekeres theorem states that, for every k, there is a number nk such that every set of nk ...
Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position ...
The following problem has been known for its beauty and elementary character. The Erd˝os Szekeres pr...
According to the Erdős–Szekeres theorem, for every n, a sufficiently large set of points in general ...
AbstractWe answer some questions of Tverberg about separability properties of families of convex set...
In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g...
According to the Erd˝os–Szekeres theorem, every set of n points in the plane contains roughly log n ...
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex posit...
Let F denote a family of pairwise disjoint convex sets in the plane. F is said to be in convex posit...
A family F of convex sets is said to be in convex position, if none of its members is contained in...
Let g(n) denote the least integer such that among any g(n) points in general position in the plane t...
Let ES(n) denote the least integer such that among any ES(n) points in general position in the plane...
Let f(k; n), n k 3, denote the smallest positive integer such that any set of f(k; n) points, in ...
Abstract. According to the Erdős-Szekeres theorem, for every n, a suffi-ciently large set of points...
AbstractIn 1935 Pál Erdős and György Szekeres proved that, roughly speaking, any configuration of n ...
The Erdős-Szekeres theorem states that, for every k, there is a number nk such that every set of nk ...
Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position ...
The following problem has been known for its beauty and elementary character. The Erd˝os Szekeres pr...
According to the Erdős–Szekeres theorem, for every n, a sufficiently large set of points in general ...
AbstractWe answer some questions of Tverberg about separability properties of families of convex set...
In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g...
According to the Erd˝os–Szekeres theorem, every set of n points in the plane contains roughly log n ...