We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...

We use the concept of production matrices to show that there exist sets of n points in the plane that admit ¿(41.77n) crossing-free geometric graphs. This improves the previously best known bound of ¿(41.18n) by Aichholzer ...

Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two ...

Let X be a finite set of points in RdRd . The Tukey depth of a point q with respect to X is the minimum number tX(q)tX(q) of points of X in a halfspace containing q. In this paper we prove a depth version of Carathéodory’s ...

A decomposition of a non-empty simple graph G is a pair [G,P] such that P is a set of non-empty induced subgraphs of G, and every edge of G belongs to exactly one subgraph in P. The chromatic index ¿'([G,P]) of a decomposition ...

Let S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that ...

This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain ...

We consider matchings with diametral disks between two sets of points R and B. More precisely, for each pair of matched points p ¿ R and q ¿ B, we consider the disk through p and q with the smallest diameter. We prove that ...