Add to ORKGCounting interior-disjoint empty convex polygons in a point set is a typical Erdős-Szekeres-type problem. We study this problem for convex 4-gons. Let P be a set of n points in the plane and in general position. A subset Q of P, with four points, is called a 4-hole in P if Q is in convex position and its convex hull does not contain any point of P in its interior. Two 4-holes in P are compatible if their interiors are disjoint. We show that P contains at least ⌊5n/11⌋−1 pairwise compatible 4-holes. This improves the lower bound of 2⌊(n − 2)/5⌋ which is implied by a result of Sakai and Urrutia (2007)
Let X be a finite set of points in the plane. We say that X is in general position if no three point...
The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, do...
Let S be a set of n points in the plane in general position, that is, no three points of S are on a ...
We consider a variant of a question of Erdős on the number of empty k-gons (k-holes) in a set of n ...
We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n p...
Let H(k; l), k ≤ l denote the smallest integer such that any set of H(k; l) points in the plane, no ...
We consider a variation of the classical Erdos-Szekeres problems on the existence and number of conv...
Let P be a set of n points in the plane in general position. A subset H of P consisting of k element...
Let S be a set of n points in the general position, that is, no three points in S are collinear. A s...
The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1,...
The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1,...
The Erdős-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of resea...
The Erdős-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of resea...
Let P be a set of n points in the plane in general position. A subset H of P consisting of k element...
Let P-n be a set of n points on the plane in general position, n >= 4. A convex quadrangulation of P...
Let X be a finite set of points in the plane. We say that X is in general position if no three point...
The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, do...
Let S be a set of n points in the plane in general position, that is, no three points of S are on a ...
We consider a variant of a question of Erdős on the number of empty k-gons (k-holes) in a set of n ...
We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n p...
Let H(k; l), k ≤ l denote the smallest integer such that any set of H(k; l) points in the plane, no ...
We consider a variation of the classical Erdos-Szekeres problems on the existence and number of conv...
Let P be a set of n points in the plane in general position. A subset H of P consisting of k element...
Let S be a set of n points in the general position, that is, no three points in S are collinear. A s...
The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1,...
The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1,...
The Erdős-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of resea...
The Erdős-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of resea...
Let P be a set of n points in the plane in general position. A subset H of P consisting of k element...
Let P-n be a set of n points on the plane in general position, n >= 4. A convex quadrangulation of P...
Let X be a finite set of points in the plane. We say that X is in general position if no three point...
The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, do...
Let S be a set of n points in the plane in general position, that is, no three points of S are on a ...