Exploració per autor "Huemer, Clemens"
Ara es mostren els items 1-20 de 37
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3-colorability of pseudo-triangulations
(2015)
Article
Accés obertDeciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-tri ... -
4-Holes in point sets
(2014-08-01)
Article
Accés obertWe 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 ... -
4-labelings and grid embeddings of plane quadrangulations
(2009-06-03)
Report de recerca
Accés obertWe show that each quadrangulation on $n$ vertices has a closed rectangle of influence drawing on the $(n-2) \times (n-2)$ grid. Further, we present a simple algorithm to obtain a straight-line drawing of a quadrangulation ... -
A new lower bound on the maximum number of plane graphs using production matrices
(2018)
Comunicació de congrés
Accés restringit per política de l'editorialWe 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 ... -
Binary labelings for plane quadrangulations and their relatives
(2010)
Article
Accés obertMotivated 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 ... -
Carathodory's theorem in depth
(2017-07-01)
Article
Accés obertLet 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 ... -
Characteristic polynomials of production matrices for geometric graphs
(2017-08-01)
Article
Accés obertAn n×n production matrix for a class of geometric graphs has the property that the numbers of these geometric graphs on up to n vertices can be read off from the powers of the matrix. Recently, we obtained such production ... -
Compatible spanning trees
(2014-07-01)
Article
Accés obertTwo plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree ... -
Edge-Removal and Non-Crossing Configurations in Geometric Graphs
(2010)
Article
Accés obertA geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for ... -
Empty monochromatic simplices
(2014-03-01)
Article
Accés obertLet 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 ... -
Empty non-convex and convex four-gons in random point sets
(2015-03-01)
Article
Accés obertLet S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty ... -
Large bichromatic point sets admit empty monochromatic 4-gons
(2009)
Text en actes de congrés
Accés obertWe 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 ... -
Lower bounds for the number of small convex k-holes
(2014-07-01)
Article
Accés obertLet S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ... -
Lower bounds on the maximum number of non-crossing acyclic graphs
(2015-08-01)
Article
Accés obertThis 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 ... -
Matching points with diametral disks
(2017)
Text en actes de congrés
Accés obertWe consider matchings between a set R of red points and a set B of blue points with diametral disks. In other words, for each pair of matched points p ¿ R and q ¿ B, we consider the diametral disk defined by p and q. We ... -
Maximizing maximal angles for plane straight-line graphs
(2013-01)
Article
Accés restringit per política de l'editorialLet G=(S,E) be a plane straight-line graph on a finite point set S⊂R2 in general position. The incident angles of a point p∈S in G are the angles between any two edges of G that appear consecutively in the circular order ... -
Modem illumination of monotone polygons
(2009)
Text en actes de congrés
Accés obertWe study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ... -
Moving rectangles
(2010)
Text en actes de congrés
Accés obertConsider a set of n pairwise disjoint axis-parallel rectangles in the plane. We call this set the source rectangles S. The aim is to move S to a set of (pairwise disjoint) target rectangles T . A move consists in a ... -
New results on production matrices for geometric graphs
(2018-07-01)
Article
Accés restringit per política de l'editorialWe present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of ... -
Note on the number of obtuse angles in point sets
(2014-09)
Article
Accés obertIn $1979$ Conway, Croft, Erd\H{o}s and Guy proved that every set $S$ of $n$ points in general position in the plane determines at least $\frac{n^3}{18}-O(n^2)$ obtuse angles and also presented a special set of $n$ points ...
