Ara es mostren els items 3-15 de 15

• Cell-paths in mono- and bichromatic line arrangements in the plane ﻿

(2014)
Text en actes de congrés
Accés obert
We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ...
• Compatible matchings in geometric graphs ﻿

(Centre de Recerca Matemàtica, 2011)
Text en actes de congrés
Accés obert
Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect ...
• Edge-Removal and Non-Crossing Configurations in Geometric Graphs ﻿

(2010)
Article
Accés obert
A 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 obert
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 ...
• Empty triangles in good drawings of the complete graph ﻿

(2015)
Article
Accés obert
A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges ...
• Geodesic order types ﻿

(2014-09-01)
Article
Accés restringit per política de l'editorial
The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained ...
• Large bichromatic point sets admit empty monochromatic 4-gons ﻿

(2009)
Text en actes de congrés
Accés obert
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 ...
• Lower bounds for the number of small convex k-holes ﻿

(2014-07-01)
Article
Accés obert
Let 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 ...
• Maximizing maximal angles for plane straight-line graphs ﻿

(2013-01)
Article
Accés restringit per política de l'editorial
Let 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 obert
We 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 ...
• On k-gons and k-holes in point sets ﻿

(2015-08-01)
Article
Accés obert
We consider a variation of the classical Erdos-Szekeres problems on the existence and number of convex k-gons and k-holes (empty k-gons) in a set of n points in the plane. Allowing the k-gons to be non-convex, we show ...
• Order types and cross-sections of line arrangements in R^3 ﻿

(2014)
Text en actes de congrés
Accés restringit per política de l'editorial
We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ...
• Two-convex polygons ﻿

(Université Libre de Bruxelles, 2009)
Text en actes de congrés
Accés obert
We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.